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Gemini-1.5 Flash on 4.OA.A.3

Common Core Standard 4.OA.A.3

This standard covers the following:

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be Interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

πŸ”— Problem

Problem: A songwriter creates a long ballad with many verses. Each verse has 162 words and he divides these into 18 lines per verse. This gives a certain number of words per line. To each line, he adds 34 more words as a refrain. What is the total number of words present in each line now?

Gemini-1.5 Flash:

Reasoning: Each verse has 162 words / 18 lines = 9 words per line.
The songwriter adds 34 words to each line, so each line now has 9 + 34 = 43 words.
### Answer: 43 

Expected answer: 43

Correct? Yes

πŸ”— Follow-up

Problem: Following from the previous problem, the songwriter then decides to add an extra refrain to the end of each verse. If the refrain has 39 words, determine how many words are in each line after this final addition.

Gemini-1.5 Flash:

Reasoning:  We already know each line has 43 words after the first refrain addition.  
The additional refrain adds 39 words to the end of each verse, but not to each line.
This extra refrain doesn't change the number of words per line.

### Answer: 43 

Expected answer: 82

Correct? No

πŸ”— Follow-up

Problem: In the previous problem, the songwriter added 34 words as the refrain to each line in his song. However, what if he had decided to keep the refrain a bit shorter and added only 28 words to each line instead? How many words would each line of the song contain in that case?

Gemini-1.5 Flash:

Reasoning: As we found earlier, each line originally had 9 words.
If the songwriter adds 28 words to each line, each line now has 9 + 28 = 37 words.
### Answer: 37 

Expected answer: 37

Correct? Yes

πŸ”— Problem

Problem: A penguin biologist counted 35 penguins on a small ice floe. In another part of the Antarctic, she counted a different group of penguins and found there were approximately 598 divided evenly among 26 ice floes. After returning to the first place, she found that the penguin population had increased by 49. Wishing to conduct another survey, she decided to take 33 more penguins into account. However, when she counted them again, she realized she had overestimated and had to subtract 10 from her calculations. Her final step was to add in the penguins she’d left at her base camp, which were 20 adults and 14 chicks. How many penguins did she count in total?

Gemini-1.5 Flash:

Reasoning: The biologist counted 598 / 26 = <<598 / 26 = 23>> 23 penguins on each of the 26 ice floes.
At the first ice floe, there were 35 + 49 = <<35 + 49 = 84>> 84 penguins.
She added 33 more penguins, making the total 84 + 33 = <<84 + 33 = 117>> 117 penguins.
After removing 10, she was left with 117 - 10 = <<117 - 10 = 107>> 107 penguins.
Finally, she added the 20 adult penguins and 14 chicks from her base camp, making the total 107 + 20 + 14 = <<107 + 20 + 14 = 141>> 141 penguins.

### Answer: 141 

Expected answer: 164

Correct? No

πŸ”— Problem

Problem: In a local park, a jungle gym has a total of 27 steps. If the top 19 steps are blue and rest along with another 19 steps are red, we get a certain number of colored steps. On another jungle gym, there are 34 green steps. What is the total number of colored steps on the two jungle gyms?

Gemini-1.5 Flash:

Reasoning: First, we need to figure out how many red steps there are on the first jungle gym. We know there are 27 total steps and 19 blue steps, so there are 27 - 19 = 8 red steps. Then we need to add the red steps to the blue steps to find the total number of colored steps on the first jungle gym: 8 + 19 = 27 colored steps. Finally, we add the number of colored steps on the first jungle gym to the number of green steps on the second jungle gym: 27 + 34 = 61 colored steps.

### Answer: 61

Expected answer: 61

Correct? Yes

πŸ”— Problem

Problem: If a cloud releases 47 millimeters of rainfall per hour over a one hour period, and the average cloud typically releases 775 millimeters of rainfall over the course of 31 hours, find the amount of rainfall from the following condition. Subtract 22 from the average rainfall of the typical cloud per hour then multiply this by 23. Add this result to a constant cloud factor of 42. Add this new result to the hourly rainfall of the initial cloud and subtract 2 from it. What is the resultant millimeters of rainfall?

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Calculate the average rainfall per hour for a typical cloud:** 775 millimeters / 31 hours = 25 millimeters/hour

2. **Subtract 22 from the average rainfall per hour:** 25 millimeters/hour - 22 millimeters/hour = 3 millimeters/hour

3. **Multiply the result by 23:** 3 millimeters/hour * 23 = 69 millimeters

4. **Add the constant cloud factor of 42:** 69 millimeters + 42 millimeters = 111 millimeters

5. **Add the result to the initial cloud's hourly rainfall:** 111 millimeters + 47 millimeters = 158 millimeters

6. **Subtract 2 from the result:** 158 millimeters - 2 millimeters = 156 millimeters

### Answer: 156 

Expected answer: 156

Correct? Yes

πŸ”— Follow-up

Problem: Now consider a different scenario where the initial cloud releases less rainfall, specifically 15 millimeters per hour over a one hour period. Keeping the other conditions from the previous problem the same (the average cloud releases 775 millimeters of rainfall over the course of 31 hours, subtract 22 from the average rainfall of the typical cloud per hour then multiply this by 23, add this result to a constant cloud factor of 42, and subtract 2 from the last result), how much rainfall would be produced in this scenario?

Gemini-1.5 Flash:

Let's follow the same steps as before, but substitute the new hourly rainfall of the initial cloud:

1. **Calculate the average rainfall per hour for a typical cloud:** 775 millimeters / 31 hours = 25 millimeters/hour

2. **Subtract 22 from the average rainfall per hour:** 25 millimeters/hour - 22 millimeters/hour = 3 millimeters/hour

3. **Multiply the result by 23:** 3 millimeters/hour * 23 = 69 millimeters

4. **Add the constant cloud factor of 42:** 69 millimeters + 42 millimeters = 111 millimeters

5. **Add the result to the initial cloud's hourly rainfall:** 111 millimeters + 15 millimeters = 126 millimeters

6. **Subtract 2 from the result:** 126 millimeters - 2 millimeters = 124 millimeters

### Answer: 124 

Expected answer: 124

Correct? Yes

πŸ”— Problem

Problem: Nadia likes to practice playing the piano. The other day she practiced for 45 minutes in the morning. In the same day, she also practiced for another 35 minutes in the afternoon and then another 35 minutes in the evening. How long did Nadia practice the piano in total that day?

Gemini-1.5 Flash:

Reasoning: Nadia practiced for a total of 45 + 35 + 35 = 115 minutes. 
### Answer: 115 

Expected answer: 115

Correct? Yes

πŸ”— Follow-up

Problem: Reflecting upon her previous practice sessions, Nadia thought she could do more. She decided to adjust her morning practice time from 45 minutes to 26 minutes. Still maintaining her afternoon and evening sessions at 35 minutes each, how many minutes in total would Nadia be practicing for the day with this adjustment?

Gemini-1.5 Flash:

Reasoning: Nadia will be practicing for a total of 26 + 35 + 35 = 96 minutes.
### Answer: 96 

Expected answer: 96

Correct? Yes

πŸ”— Problem

Problem: A popular clothing store sells dresses for $44 each. During a flash sale, they further reduce prices by a factor of 465 divided by 31. How much does a dress cost during the flash sale?

Gemini-1.5 Flash:

Reasoning: The sale reduces the price by 465/31 = <<465/31=15>>15 dollars.
The final price is $44 - $15 = <<44-15=29>>29 dollars.
### Answer: $29 

Expected answer: 660

Correct? No

πŸ”— Problem

Problem: A rope maker made 46 meters of rope on Monday. On Tuesday, he made as many meters of rope as he did on Monday, plus an additional 19 meters. However, by Wednesday, 9 meters of this rope had been damaged and was unusable. How many meters of usable rope does he have after Wednesday?

Gemini-1.5 Flash:

Reasoning: On Tuesday, the rope maker made 46 + 19 = <<46+19=65>> 65 meters of rope.
Therefore, he made a total of 46 + 65 = <<46+65=111>> 111 meters of rope over Monday and Tuesday.
After Wednesday, he has 111 - 9 = <<111-9=102>> 102 meters of usable rope.
### Answer: 102 

Expected answer: 56

Correct? No

πŸ”— Problem

Problem: Juliana bought 16 pairs of vintage earrings for a gift. Each pair costs $2. She also chose a special jewelry box that costs $25. In addition, she paid $48 for the gift wrapping service. How much did she spend in total for her gift?

Gemini-1.5 Flash:

Reasoning: Juliana spent 16 * $2 = $32 on the earrings.
She spent $32 + $25 + $48 = $105 in total for her gift.
### Answer: $105 

Expected answer: 105

Correct? Yes

πŸ”— Problem

Problem: If Emma takes 60 beads and divides them equally among 3 of her friends, each friend will get a certain number of beads. She then adds 4 more beads to each friend's pile to start making necklaces. How many beads does each friend have now?

Gemini-1.5 Flash:

Reasoning: Emma divides 60 beads by 3 friends, giving each friend 60/3 = 20 beads.
She then adds 4 beads to each pile, so each friend now has 20 + 4 = 24 beads. 
### Answer: 24 

Expected answer: 24

Correct? Yes

πŸ”— Follow-up

Problem: After distributing the beads among her friends, Emma realizes that she actually wanted to divide her 60 beads evenly among 28 friends instead of 3. She recalculates and then adds 4 more beads to each friend's stack after the initial division. How many beads does each friend have now?

Gemini-1.5 Flash:

Reasoning: Emma has 60 beads and wants to divide them among 28 friends, giving each friend 60/28 = 2.14 beads (approximately). Since you can't have a fraction of a bead, each friend would get 2 beads. 
Then, Emma adds 4 beads to each friend's pile, so each friend now has 2 + 4 = 6 beads.

### Answer: 6 

Expected answer: 43/7

Correct? No

πŸ”— Problem

Problem: A young boy with a creative mind decided to build a kite. He started with 37 paper straws but decided that 4 were unnecessary and removed them. Later, he realized his kite was still too bulky and removed another 23 straws. He multiplied the remaining number of straws by 45, subtracted 49 from that total, and then took out 7 more straws. How many straws did the boy have left?

Gemini-1.5 Flash:

Here's how we can solve this problem step-by-step:

1. **Start with the initial number:** The boy began with 37 straws.
2. **Remove the first set:** He removed 4 straws, leaving him with 37 - 4 = 33 straws.
3. **Remove the second set:** He then removed another 23 straws, leaving him with 33 - 23 = 10 straws.
4. **Multiply by 45:** He multiplied the remaining straws by 45, giving him 10 * 45 = 450 straws.
5. **Subtract 49:** He then subtracted 49 from this total, leaving him with 450 - 49 = 401 straws.
6. **Remove the final set:** Finally, he removed 7 more straws, leaving him with 401 - 7 = 394 straws.

### Answer: 394 

Expected answer: 394

Correct? Yes

πŸ”— Follow-up

Problem: After reflecting on his kite design, the young boy realized he made a mistake. When he multiplied the number of remaining paper straws by 45, he should have subtracted 25, not 49. If he corrects this calculation error and takes out 7 final straws as before, how many straws does he have now for his kite?

Gemini-1.5 Flash:

Let's retrace the steps, correcting the multiplication error:

1. **Start with the initial number:** The boy began with 37 straws.
2. **Remove the first set:** He removed 4 straws, leaving him with 37 - 4 = 33 straws.
3. **Remove the second set:** He then removed another 23 straws, leaving him with 33 - 23 = 10 straws.
4. **Multiply by 45:** He multiplied the remaining straws by 45, giving him 10 * 45 = 450 straws.
5. **Subtract 25 (correcting the mistake):**  He then subtracted 25 from this total, leaving him with 450 - 25 = 425 straws.
6. **Remove the final set:** Finally, he removed 7 more straws, leaving him with 425 - 7 = 418 straws.

### Answer: 418 

Expected answer: 418

Correct? Yes

πŸ”— Problem

Problem: At the zoo, there were 2 trips being hosted. Each trip was allowed to see 2 animals. However, each animal had 3 baby animals with them, making the number of animals seen per trip multiplied by 3. If each baby animal could be photographed 21 times, how many photos could be taken in total? Also, if 34 photos were spoiled and unusable out of the entire batch, but guests were given the opportunity to take an additional 30 photos later, how many usable photos would there be in total?

Gemini-1.5 Flash:

Reasoning: Each trip sees 2 animals * 3 baby animals per animal = 6 baby animals.
There were 2 trips * 6 baby animals per trip = 12 baby animals seen.
A total of 12 baby animals * 21 photos per baby animal = 252 photos were taken.
Out of the 252 photos, 252 photos - 34 spoiled photos = 218 photos were usable.
The guests took an additional 30 photos, bringing the usable photos to 218 photos + 30 photos = 248 usable photos.
### Answer: 248

Expected answer: 248

Correct? Yes

πŸ”— Follow-up

Problem: In the previous case at the zoo, imagine if each baby animal could only be photographed 16 times, instead of 21. Given the same spoiling rate of 34 photos and the additional opportunity to take 30 more photos later, how many usable photos would be available now?

Gemini-1.5 Flash:

Reasoning: Each trip sees 2 animals * 3 baby animals per animal = 6 baby animals.
There were 2 trips * 6 baby animals per trip = 12 baby animals seen.
A total of 12 baby animals * 16 photos per baby animal = 192 photos were taken.
Out of the 192 photos, 192 photos - 34 spoiled photos = 158 photos were usable.
The guests took an additional 30 photos, bringing the usable photos to 158 photos + 30 photos = 188 usable photos.
### Answer: 188

Expected answer: 188

Correct? Yes

πŸ”— Problem

Problem: In a literacy event, a group of learners were asked to write a word from letters. In the first round, they could form a word with 47 letters, but due to a mistake, they had to remove 30 letters. Then, they figured out they could still add 10 more letters to this word. In the next round, they removed 3 of these letters from the updated word. How many letters were there in the word after this last deletion?

Gemini-1.5 Flash:

Reasoning: After removing 30 letters, the word had 47 - 30 = 17 letters. 
Then, they added 10 letters, making the word have 17 + 10 = 27 letters. 
Finally, they removed 3 letters, leaving the word with 27 - 3 = 24 letters.

### Answer: 24 

Expected answer: 24

Correct? Yes

πŸ”— Follow-up

Problem: In the continuation of the literacy event, the learners had the opportunity to add more letters to the word after the last deletion. They decided to add 39 more letters. How many letters were in the word after this final addition?

Gemini-1.5 Flash:

Reasoning: After the last deletion, the word had 24 letters. 
They then added 39 more letters, bringing the total to 24 + 39 = 63 letters.

### Answer: 63 

Expected answer: 63

Correct? Yes

πŸ”— Follow-up

Problem: In revisiting the literacy event, let's consider a different scenario. When the learners formed the word with 47 letters and due to a mistake had to remove 30, instead of adding 10 letters, what if they added only 10 - 16 = -6 letters? What would the total number of letters be in the word after this change?

Gemini-1.5 Flash:

Reasoning: After removing 30 letters, the word had 47 - 30 = 17 letters.
Then, they added -6 letters, which means they actually removed 6 letters, leaving the word with 17 - 6 = 11 letters. 

### Answer: 11 

Expected answer: 11

Correct? Yes

πŸ”— Problem

Problem: A turtle named Tommy moves at 74/37 miles per hour. If Tommy maintains his current speed for a while then slows down by 3 mph, then speeds up to his initial speed again, what would be his average speed?

Gemini-1.5 Flash:

Here's how we can solve this problem:

* **Simplify Tommy's initial speed:**  74/37 simplifies to 2 miles per hour.
* **Tommy's slower speed:**  His slower speed is 2 mph - 3 mph = -1 mph. This means he's actually moving backward at 1 mph.
* **Average speed calculation:** To calculate the average speed, we need to consider the time spent at each speed. Since we don't know the time, we'll assume he spends an equal amount of time at each speed. This makes the calculation easier.
* **Average speed formula:**  Average speed = (Total distance) / (Total time)
* **Simplified approach:** Since we're assuming equal time at each speed, we can simply average the three speeds: (2 mph + (-1 mph) + 2 mph) / 3 = 1 mph

### Answer: 1 

Expected answer: 1

Correct? Yes

πŸ”— Problem

Problem: Liam has 40 sets of building blocks. Each set contains 16 blocks. How many building blocks does Liam have in total?

Gemini-1.5 Flash:

Reasoning: Liam has 40 * 16 = 640 building blocks in total.
### Answer: 640 

Expected answer: 640

Correct? Yes

πŸ”— Follow-up

Problem: After counting all the building blocks, Liam decides to give away 25 to his friend. How many building blocks does Liam have left after giving some to his friend?

Gemini-1.5 Flash:

Reasoning: Liam has 640 - 25 = 615 building blocks left.
### Answer: 615 

Expected answer: 615

Correct? Yes

πŸ”— Follow-up

Problem: What if Liam only had 38 sets of building blocks instead of 40? How many building blocks would he have in that case?

Gemini-1.5 Flash:

Reasoning: If Liam has 38 sets of building blocks, he has 38 * 16 = 608 building blocks.

### Answer: 608 

Expected answer: 608

Correct? Yes

πŸ”— Problem

Problem: John has 24 pencils. Then he bought more such that the number of pencils he has now is equal to the number of what he had plus 7. How many pencils does John have now?

Gemini-1.5 Flash:

Reasoning: John has 24 + 7 = 31 pencils now.
### Answer: 31 

Expected answer: 31

Correct? Yes

πŸ”— Follow-up

Problem: After having a total of 31 pencils, John received a gift box with an additional 26 pencils. How many pencils does he have now?

Gemini-1.5 Flash:

Reasoning: John now has 31 + 26 = 57 pencils.
### Answer: 57 

Expected answer: 57

Correct? Yes

πŸ”— Follow-up

Problem: Suppose originally, John only had 2 pencils instead of 24 and then he bought more such that the number of pencils he has now is equal to the number of pencils he had plus 7. How many pencils does John have now?

Gemini-1.5 Flash:

Reasoning: John now has 2 + 7 = 9 pencils.
### Answer: 9 

Expected answer: 9

Correct? Yes

πŸ”— Problem

Problem: The snowfall in City A, which lasts for 50 days, is currently 36 days in. In City B, there is a unique snow pattern where for every 14 days, it snows 98 inches. The total snowfall in inches in City A is expected to be the product of the remaining snowfall days in City A and the average daily snowfall in inches in City B. However, the snow removal has been keeping up and has managed to remove an amount of snow equal to the average daily snowfall in City B. How much snow in inches is left in City A after the snow removal?

Gemini-1.5 Flash:

Here's how we can solve this problem step-by-step:

1. **Remaining snowfall days in City A:** City A has 50 - 36 = 14 days of snowfall remaining.

2. **Average daily snowfall in City B:** City B snows 98 inches every 14 days, so the average daily snowfall is 98 / 14 = 7 inches.

3. **Total expected snowfall in City A:** The total expected snowfall is 14 days * 7 inches/day = 98 inches.

4. **Snow removed:** The snow removal has removed 7 inches of snow.

5. **Snow left in City A:** The amount of snow left in City A is 98 inches - 7 inches = 91 inches.

### Answer: 91 

Expected answer: 91

Correct? Yes

πŸ”— Problem

Problem: A pirate finds 28 rubies on the first day of his treasure hunt. On the second day, he finds another haul of rubies equal to the first day's find plus an additional 21 rubies. How many rubies does the pirate have in total after the second day?

Gemini-1.5 Flash:

Reasoning: On the second day, the pirate finds 28 + 21 = <<28 + 21 = 49>> 49 rubies.
In total, he has 28 + 49 = <<28 + 49 = 77>> 77 rubies after the second day.
### Answer: 77 

Expected answer: 77

Correct? Yes

πŸ”— Follow-up

Problem: After the second day, the pirate continues his adventure and stumbles upon a third treasure chest containing 29 additional rubies. Unfortunately, he drops and loses 36 rubies while escaping a group of rival pirates. How many rubies does he have in total now?

Gemini-1.5 Flash:

Reasoning: After finding the third treasure chest, the pirate has 77 + 29 = <<77 + 29 = 106>> 106 rubies.
After losing some rubies, he has 106 - 36 = <<106 - 36 = 70>> 70 rubies.
### Answer: 70 

Expected answer: 70

Correct? Yes

πŸ”— Follow-up

Problem: After reflecting on his loss, the pirate remembers that, on the first day, he actually only found 6 rubies, not 28. On the second day, he still found a number of rubies equal to what he found on the first day plus an additional 21 rubies. How many rubies did the pirate have in total after the second day, taking this into account?

Gemini-1.5 Flash:

Reasoning: On the second day, the pirate found 6 + 21 = <<6 + 21 = 27>> 27 rubies.
In total, he has 6 + 27 = <<6 + 27 = 33>> 33 rubies after the second day.
### Answer: 33 

Expected answer: 33

Correct? Yes

πŸ”— Problem

Problem: There were 47 inches of snowfall in January and an additional 7 inches in early February. On February 15th, there was an additional 17 inches of snowfall. Then, 48 inches of snow fell in March. In April, we had an additional 31 inches of snowfall early on, but then 27 inches melted by the end of the month. How many inches of snow does this sum up to at the end of April?

Gemini-1.5 Flash:

Let's break down the snowfall and melting:

* **January:** 47 inches
* **February:** 7 inches (early) + 17 inches (Feb 15th) = 24 inches
* **March:** 48 inches
* **April:** 31 inches (early) - 27 inches (melted) = 4 inches

Now, let's add up all the snowfall:

47 inches + 24 inches + 48 inches + 4 inches = 123 inches

### Answer: 123 

Expected answer: 123

Correct? Yes

πŸ”— Follow-up

Problem: Following the same snowfall pattern, but this time if April were to receive a slightly higher snowfall, with an additional 44 inches of snowfall early on, but then 27 inches melted by the end of the month, how many inches of snow would this sum up to at the end of April now?

Gemini-1.5 Flash:

Let's break down the snowfall and melting:

* **January:** 47 inches
* **February:** 7 inches (early) + 17 inches (Feb 15th) = 24 inches
* **March:** 48 inches
* **April:** 44 inches (early) - 27 inches (melted) = 17 inches

Now, let's add up all the snowfall:

47 inches + 24 inches + 48 inches + 17 inches = 136 inches

### Answer: 136 

Expected answer: 136

Correct? Yes

πŸ”— Problem

Problem: At a fair, a vendor sold balloons. On a particularly busy day, he sold 46 balloons every hour for 11 hours straight. After the fair had closed, he ended up selling an additional 31 balloons to some stragglers. How many balloons did he sell in total that day?

Gemini-1.5 Flash:

Reasoning: The vendor sold 46 x 11 = <<46*11=506>> 506 balloons during the fair hours.
In total, the vendor sold 506 + 31 = <<506+31=537>> 537 balloons that day.

### Answer: 537 

Expected answer: 537

Correct? Yes

πŸ”— Problem

Problem: Mary and John decided to play a game of cards. In the first game, Mary scored 31 points and John scored 39 points. In the second game, their combined score was increased by 35 more points. During a special round, they could multiply their score by the difference between 27 and the number of cards left in the deck, which was 23. What was their final score in the special round?

Gemini-1.5 Flash:

Reasoning: Their combined score in the first two games was 31 + 39 = 70 points.
Their combined score increased by 35 points, making it 70 + 35 = 105 points.
The difference between 27 and the number of cards left in the deck is 27 - 23 = 4.
Their final score in the special round is 105 * 4 = 420 points. 
### Answer: 420 

Expected answer: 420

Correct? Yes

πŸ”— Follow-up

Problem: After the special round in their card game, Mary and John discovered two extra points they hadn't accounted for earlier. After adding these extra points to their score, what was their final combined score?

Gemini-1.5 Flash:

Reasoning: Their final score in the special round was 420 points.
They discovered two extra points, so their final combined score is 420 + 2 = 422 points.

### Answer: 422 

Expected answer: 422

Correct? Yes

πŸ”— Follow-up

Problem: Given the same card game situation, suppose that in the second game, Mary and John’s combined score increased by 50 points instead of 35. Following the same rule in their special round, where they multiplied their score by the difference between 27 and the number of cards left in the deck (which was 23), what would their final score be in this case?

Gemini-1.5 Flash:

Reasoning: Their combined score in the first two games was 31 + 39 = 70 points.
Their combined score increased by 50 points, making it 70 + 50 = 120 points.
The difference between 27 and the number of cards left in the deck is 27 - 23 = 4.
Their final score in the special round is 120 * 4 = 480 points. 
### Answer: 480 

Expected answer: 480

Correct? Yes

πŸ”— Problem

Problem: A furniture company manufactured 17 upholstered seats and 18 wooden seats in the morning, and then produced another 29 in the afternoon. They repeated this production in the evening. Later on, they gave away 48 chairs to charity and used 7 chairs for quality testing. How many chairs are left after these operations?

Gemini-1.5 Flash:

Reasoning: The furniture company produced a total of 17 + 18 = 35 seats in the morning.
They produced a total of 35 + 29 = 64 seats in the morning and afternoon.
They produced a total of 64 * 2 = 128 seats in a day.
They had 128 - 48 - 7 = 73 seats left.
### Answer: 73

Expected answer: 73

Correct? Yes

πŸ”— Follow-up

Problem: Continuing from the last example, suppose the furniture company only crafted 15 wooden seats in the morning instead of 18 but kept the rest of operations unchanged. After repeating the same production, donating 48 chairs to charity, and using 7 for quality testing, how many chairs will be the company left with?

Gemini-1.5 Flash:

Reasoning: The furniture company produced a total of 17 + 15 = 32 seats in the morning.
They produced a total of 32 + 29 = 61 seats in the morning and afternoon.
They produced a total of 61 * 2 = 122 seats in a day.
They had 122 - 48 - 7 = 67 seats left.

### Answer: 67

Expected answer: 67

Correct? Yes

πŸ”— Problem

Problem: On a popular jungle gym, there are 46 monkey bars and 18 swinging ropes for the kids to play on. Nearby, a larger jungle gym was recently built to accommodate more kids. The new jungle gym contains 2 extra long zip lines and 20 regular zip lines, each requiring 31 special hooks to install. How many more hooks were used in the new jungle gym compared to the number of play components on the popular jungle gym?

Gemini-1.5 Flash:

Reasoning: The new jungle gym has 2+20 = 22 zip lines.
In total, the new jungle gym has 22*31 = 682 hooks.
The popular jungle gym has 46+18 = 64 play components.
The new jungle gym used 682-64 = 618 more hooks. 
### Answer: 618 

Expected answer: 618

Correct? Yes

πŸ”— Problem

Problem: John has saved $168 and he decides to divide it evenly between 21 days. After doing so, he then gets an additional $47 from his job. He then receives another amount of money which is the sum of $12 and $45. How much money does John have now?

Gemini-1.5 Flash:

Reasoning: John divides his savings evenly by 21 days, meaning he spends $168/21 = $8 per day. 
After getting paid, he has $168 + $47 = $215.
Then he receives another $12 + $45 = $57.
Finally, John has a total of $215 + $57 = $272.
### Answer: 272 

Expected answer: 112

Correct? No

πŸ”— Problem

Problem: A robot can stack 32 boxes in 1 minute. If it works non-stop for 4 minutes and then picks up 1 extra box, how many boxes will this robot have stacked in total?

Gemini-1.5 Flash:

Reasoning: The robot stacks 32 boxes per minute, so in 4 minutes it stacks 32*4 = 128 boxes.
After that, the robot picks up one more box, for a total of 128+1 = 129 boxes.
### Answer: 129 

Expected answer: 129

Correct? Yes

πŸ”— Follow-up

Problem: After stacking boxes for 4 minutes, the robot takes a break. When it comes back, it accidentally knocks over 21 of the boxes. How many boxes remain stacked after the robot knocks some over?

Gemini-1.5 Flash:

Reasoning: We know the robot stacked 128 boxes before taking a break. After knocking over 21 boxes, there are 128-21 = 107 boxes left.
### Answer: 107 

Expected answer: 108

Correct? No

πŸ”— Follow-up

Problem: Let's consider a different scenario: If, instead of picking up an extra single box after 4 minutes, the robot picked up an extra 11 boxes, how many boxes would this robot have stacked in total?

Gemini-1.5 Flash:

Reasoning: The robot stacks 32 boxes per minute, so in 4 minutes it stacks 32*4 = 128 boxes.
After that, the robot picks up 11 more boxes, for a total of 128+11 = 139 boxes.
### Answer: 139 

Expected answer: 139

Correct? Yes

πŸ”— Problem

Problem: A female tiger gave birth to 26 cubs in all her lifetime. Unfortunately, 17 of them did not survive the harsh conditions of the wild. However, after growing up, 6 of the surviving tigers moved to other territories. How many tigers remained in the female tiger's territory?

Gemini-1.5 Flash:

Reasoning: First, we need to figure out how many cubs survived: 26 cubs - 17 cubs = 9 cubs
Then, we subtract the tigers that moved away: 9 cubs - 6 cubs = 3 cubs
### Answer: 3 

Expected answer: 3

Correct? Yes

πŸ”— Follow-up

Problem: Suppose that originally the female tiger had given birth to 24 cubs instead of 26 in her lifetime, and the same number of 17 cubs had not survived the harsh conditions of the wild. If the same number of surviving tigers, 6, moved to other territories, how many tigers would have remained in the female tiger's territory?

Gemini-1.5 Flash:

Reasoning: First, we find the number of cubs that survived: 24 cubs - 17 cubs = 7 cubs. 
Then, we subtract the tigers that moved away: 7 cubs - 6 cubs = 1 cub.
### Answer: 1 

Expected answer: 1

Correct? Yes

πŸ”— Problem

Problem: A colony of penguins originally started with 44 members. After a while, 39 new penguins join the colony. Later, from that group, 16 penguins leave to start a new colony elsewhere. To supplant the loss, another group of 35 penguins join the colony. How many penguins are in the colony now?

Gemini-1.5 Flash:

Reasoning: The colony started with 44 penguins, and then 39 more joined, making a total of 44+39 = 83 penguins. 
Later, 16 penguins left, reducing the number to 83-16 = 67 penguins. 
Finally, 35 more penguins joined, making the final number 67+35 = 102 penguins. 
### Answer: 102 

Expected answer: 102

Correct? Yes

πŸ”— Follow-up

Problem: In the same penguin colony, they started off with 44 members. After a while, 39 new penguins join the colony. Later, from that group, 16 penguins leave to start a new colony elsewhere. This time, to supplant the loss, another group of 12 penguins join the colony, instead of 35. How many penguins are in the colony now?

Gemini-1.5 Flash:

Reasoning: The colony started with 44 penguins, and then 39 more joined, making a total of 44+39 = 83 penguins. 
Later, 16 penguins left, reducing the number to 83-16 = 67 penguins. 
Finally, 12 more penguins joined, making the final number 67+12 = 79 penguins. 
### Answer: 79 

Expected answer: 79

Correct? Yes

πŸ”— Problem

Problem: A helicopter travels 10 miles in one minute. If the helicopter increases its speed by 40 miles, plus another 20 miles, how far will the helicopter travel in 12 minutes at this increased speed?

Gemini-1.5 Flash:

Reasoning: First, we need to calculate the helicopter's increased speed. The helicopter increases its speed by 40 miles + 20 miles = 60 miles.
Then, the helicopter's new speed is 10 miles + 60 miles = 70 miles per minute. 
So, in 12 minutes, the helicopter will travel 70 miles/minute * 12 minutes = 840 miles. 
### Answer: 840 

Expected answer: 840

Correct? Yes

πŸ”— Follow-up

Problem: After re-evaluating its performance, the helicopter realized that its actual speed increase was lesser than initially thought. Instead of the initial 40 miles speed increase, the increase was just 2 miles. Given that the original speed of 10 miles and an additional bonus speed of 20 miles remained the same, how far will the helicopter be able to travel in 12 minutes at this revised speed?

Gemini-1.5 Flash:

Reasoning: The helicopter's new speed is 10 miles (original speed) + 2 miles (revised increase) + 20 miles (bonus) = 32 miles per minute. 
Therefore, in 12 minutes, the helicopter will travel 32 miles/minute * 12 minutes = 384 miles. 
### Answer: 384 

Expected answer: 384

Correct? Yes

πŸ”— Problem

Problem: A new telescope has a magnification power of 26. To further explore the universe, another telescope is required that needs to be exactly 41 in magnification strength. How much more magnification is required for the new telescope compared to the existing one?

Gemini-1.5 Flash:

Reasoning: To find the difference in magnification, subtract the magnification of the existing telescope from the required magnification of the new telescope: 41 - 26.

### Answer: 15 

Expected answer: 15

Correct? Yes

πŸ”— Follow-up

Problem: The Space Institute realized that the initial magnification power of the existing telescope was actually 16, not 26 as previously thought. If they still want to reach a magnification strength of 41, how much more magnification is now needed compared to the existing telescope?

Gemini-1.5 Flash:

Reasoning: To find the difference in magnification, subtract the magnification of the existing telescope from the required magnification of the new telescope: 41 - 16.

### Answer: 25 

Expected answer: 25

Correct? Yes

πŸ”— Problem

Problem: Sophie's parents give her $18 for every hour she works at the family business. On Monday, she worked 2 of those hours. Then she bought a $4 ice cream and another $4 coffee afterwards. She then added Monday's leftover amount to her pay for her next single hour of work. After that, she got an additional $45 as a bonus from her grandmother. How much money does Sophie have in total now?

Gemini-1.5 Flash:

Reasoning: Sophie earned $18*2 = $36 from working 2 hours on Monday.
After buying ice cream and coffee, Sophie had $36 - $4 - $4 = $28 left.
Sophie earned another $18 for her next hour of work.
Adding that to her leftover amount, Sophie had $28 + $18 = $46.
Her grandmother's bonus increased her money to $46 + $45 = $91.
### Answer: 91 

Expected answer: 91

Correct? Yes

πŸ”— Follow-up

Problem: In the same scenario, imagine if Sophie's parents now give her $5 for every hour she works at the family business instead of $18. She still works for two hours on Monday, spends the same amount on ice cream and coffee, works an additional hour, and receives the same $45 bonus from her grandmother. How much money does Sophie have in total now?

Gemini-1.5 Flash:

Reasoning: Sophie now earns $5*2 = $10 from working 2 hours on Monday.
After buying ice cream and coffee, Sophie has $10 - $4 - $4 = $2 left.
Sophie earns another $5 for her next hour of work.
Adding that to her leftover amount, Sophie has $2 + $5 = $7.
Her grandmother's bonus increased her money to $7 + $45 = $52.
### Answer: 52 

Expected answer: 52

Correct? Yes

πŸ”— Problem

Problem: A towel company initially produced 30 beach towels and 6 hand towels. They then gave away 7 towels for charity, which leaves a certain amount of towels. They then decided to produce 14 more towels to add to their current stock. On the other hand, they made a special batch of 13 towels for every towel left after their charity activity and deducted 19 towels from this special batch, calling it their premium collection. They then noted 20 towels were damaged and removed it from this premium collection. After this, they deducted 3 more towels from the remaining premium collection and combined it with the total they had after their second batch of production. How many towels does the company have now?

Gemini-1.5 Flash:

Here's how to break down the problem step-by-step:

1. **Initial Production:** The company started with 30 beach towels + 6 hand towels = 36 towels.

2. **Charity:** After giving away 7 towels, they have 36 - 7 = 29 towels left.

3. **Second Batch:** After producing 14 more towels, they have 29 + 14 = 43 towels.

4. **Special Batch:** They made 13 towels for each of the 29 towels left after charity, so they made 13 * 29 = 377 towels.

5. **Premium Collection:** They deducted 19 towels from the special batch, leaving 377 - 19 = 358 towels.

6. **Damaged Towels:** After removing damaged towels, they have 358 - 20 = 338 towels in the premium collection.

7. **Final Deduction:** After deducting 3 more towels, the premium collection has 338 - 3 = 335 towels.

8. **Total:**  The company now has 43 towels (from their initial production and second batch) + 335 towels (from the premium collection) = 378 towels.

### Answer: 378 

Expected answer: 378

Correct? Yes

πŸ”— Problem

Problem: An extraterrestrial being from the planet Zorkon communicates that they have 50 special energy crystals. Then they explain that they'll get 20 more energy crystals in a few earth days. Additionally, their zorbcraft has a hidden compartment that contains 50 energy crystals and 6 extra lumino-gems, and they plan to add the upcoming energy crystals to this compartment as well. How many items (including both energy crystals and lumino-gems) would be in the zorbcraft's compartment at that time?

Gemini-1.5 Flash:

Here's how we can solve this:

1. **Initial crystals:** The zorbcraft starts with 50 energy crystals.
2. **New crystals:** They'll get 20 more energy crystals.
3. **Total crystals:** This means they'll have 50 + 20 = 70 energy crystals.
4. **Total items:**  Adding the initial 50 crystals and the 6 lumino-gems, the compartment will have 70 + 6 = 76 items.

### Answer: 76 

Expected answer: 126

Correct? No

πŸ”— Problem

Problem: A park contains 43 Velociraptors. Then, the park added another set of dinosaurs which numbered 972, but as it so happens, each of these sections contained 27 dinosaurs. This meant the actual number of new dinosaur types added was less. After calculating the new dinosaur types, they found out that the number of Velociraptors was more. They found the difference and multiplied this difference by 7, as each of the Velociraptors laid 7 new eggs that week. How many total eggs were laid by the Velociraptors that week?

Gemini-1.5 Flash:

Reasoning: The park added 972/27 = <<972/27=36>> 36 new dinosaur types.
The difference between the number of Velociraptors and new dinosaur types is 43-36 = <<43-36=7>> 7.
Therefore, the Velociraptors laid 7*7 = <<7*7=49>> 49 eggs that week.
### Answer: 49 

Expected answer: 49

Correct? Yes

πŸ”— Follow-up

Problem: Following up from the previous scenario, the park's wardens discovered that 46 of the eggs laid by the Velociraptors were not fertilized and not going to hatch. What is the number of Velociraptor eggs that are expected to successfully hatch?

Gemini-1.5 Flash:

Reasoning: The number of Velociraptor eggs expected to hatch is 49-46 = <<49-46=3>> 3.
### Answer: 3 

Expected answer: 3

Correct? Yes

πŸ”— Follow-up

Problem: Continuing off the previous scenario, the wardens realized that they had made a mistake in their calculations. Each box actually contained 46 dinosaurs, not 27. If this was the case, how many total eggs are expected to be laid by the Velociraptors this week?

Gemini-1.5 Flash:

Reasoning: The park actually added 972/46 = <<972/46=21.13>> 21 new dinosaur types (we round down as we can't have a fraction of a type).
The difference between the number of Velociraptors and new dinosaur types is 43-21 = <<43-21=22>> 22.
Therefore, the Velociraptors laid 22*7 = <<22*7=154>> 154 eggs that week. 
### Answer: 154 

Expected answer: 3521/23

Correct? No

πŸ”— Problem

Problem: There is a bowl containing 46 oranges. After Maria took 16 oranges from that bowl, how many oranges are left?

Gemini-1.5 Flash:

Reasoning: Maria took 16 oranges, so there are 46 - 16 = 30 oranges left in the bowl.
### Answer: 30 

Expected answer: 30

Correct? Yes

πŸ”— Follow-up

Problem: Initially, Maria believed the bowl contained 46 oranges, but soon she realized her mistake and found out there were actually 49 in total. With this new information, after taking out 16 oranges, how many are left now in the bowl?

Gemini-1.5 Flash:

Reasoning:  Maria initially thought there were 46 oranges, but there were actually 49.  So, after taking out 16, there are 49 - 16 = 33 oranges left in the bowl.

### Answer: 33 

Expected answer: 33

Correct? Yes

πŸ”— Problem

Problem: A toothbrush factory produces 37 toothbrushes per minute at the start of its morning shift. A little later, it increases its production to rate to 308 toothbrushes every 7 minutes. If this increased rate of production continued for 16 minutes, how many toothbrushes were produced in total?

Gemini-1.5 Flash:

Reasoning: First, we find the number of toothbrushes produced per minute at the higher rate: 308 toothbrushes / 7 minutes = 44 toothbrushes per minute.
Then, we multiply this rate by the number of minutes the factory ran at this rate: 44 toothbrushes/minute * 16 minutes = 704 toothbrushes.
To find the total, we add the number of toothbrushes produced at the original rate to the number produced at the higher rate.  We need to calculate the number of toothbrushes produced in the first 7 minutes at the higher rate (as the problem starts at the higher rate after 7 minutes).  
In those first 7 minutes at the higher rate, 44 toothbrushes/minute * 7 minutes = 308 toothbrushes were produced.  This leaves 9 minutes at the lower production rate (16 minutes total - 7 minutes at the higher rate).
The total number of toothbrushes produced in those 9 minutes at the lower rate: 37 toothbrushes/minute * 9 minutes = 333 toothbrushes.
The total number of toothbrushes produced over the entire 16 minute period is: 333 toothbrushes + 704 toothbrushes = 1037 toothbrushes.
### Answer: 1037 

Expected answer: 741

Correct? No

πŸ”— Problem

Problem: A research laboratory has 39 telescopes initially. They added 7 more telescopes in the first month and then 17 more in the second month. Twelve more telescopes arrived in the third month, followed by further add up of 18 in the fourth month. In fifth month, they got exactly the same number of telescopes as they had initially i.e. 39 telescopes and in the sixth month, they received extra 19 telescopes. How many telescopes does the research laboratory have at the end of the sixth month.

Gemini-1.5 Flash:

Here's how to calculate the total number of telescopes:

* **Initial telescopes:** 39
* **Month 1:** +7 telescopes
* **Month 2:** +17 telescopes
* **Month 3:** +12 telescopes
* **Month 4:** +18 telescopes
* **Month 5:** +39 telescopes 
* **Month 6:** +19 telescopes

**Total telescopes:** 39 + 7 + 17 + 12 + 18 + 39 + 19 = **141**

### Answer: 141 

Expected answer: 151

Correct? No

πŸ”— Problem

Problem: A table was initially set with 20 forks and 23 knives. Later in the day, 28 more sets of cutlery were added, each set containing 26 utensils. After counting, they found 7 more utensils than expected. However, there were 46 missing utensils, and they had to remove the original set of 20 forks and 23 knives. How many utensils were left on the table?

Gemini-1.5 Flash:

Here's how we can solve this step-by-step:

1. **Calculate the number of utensils added:** 28 sets * 26 utensils/set = 728 utensils
2. **Calculate the expected total utensils:** 20 forks + 23 knives + 728 utensils = 771 utensils
3. **Calculate the actual total utensils:** 771 utensils + 7 utensils = 778 utensils
4. **Calculate the total utensils before removing the original set:** 778 utensils + 46 utensils = 824 utensils
5. **Calculate the number of utensils remaining after removing the original set:** 824 utensils - 20 forks - 23 knives = 781 utensils

### Answer: 781 

Expected answer: 646

Correct? No

πŸ”— Problem

Problem: A magical unicorn has 50 red roses and 36 blue roses in her mystical garden. But then, a storm comes and 25 blue roses are destroyed. How many roses does the unicorn have left in her garden after the storm?

Gemini-1.5 Flash:

Reasoning: The unicorn had 36 - 25 = <<36-25=11>> 11 blue roses left after the storm. 
Therefore, the unicorn had a total of 50 + 11 = <<50+11=61>> 61 roses left in her garden.
### Answer: 61 

Expected answer: 61

Correct? Yes

πŸ”— Follow-up

Problem: After the storm, the magical unicorn plants 41 more pink roses in her mystical garden. How many roses does the unicorn have in her garden now?

Gemini-1.5 Flash:

Reasoning: The unicorn had 61 roses after the storm and then planted 41 more pink roses. So, now she has 61 + 41 = <<61+41=102>> 102 roses in her garden.
### Answer: 102 

Expected answer: 102

Correct? Yes

πŸ”— Follow-up

Problem: Originally, the magical unicorn had 50 red roses and 36 blue roses in her mystical garden. But if she had initially had 50 red roses and 38 blue roses instead, and still lost 25 roses in the storm, how many roses would she have left in her garden after the storm?

Gemini-1.5 Flash:

Reasoning: After the storm, the unicorn would have 38 - 25 = <<38-25=13>> 13 blue roses left.
In total, the unicorn would have 50 + 13 = <<50+13=63>> 63 roses left in her garden. 
### Answer: 63 

Expected answer: 63

Correct? Yes

πŸ”— Problem

Problem: A factory produces 100 bottles every hour. Half of the hourly production is sent to one warehouse. At another location, triple the amount sent to the first warehouse was marked for shipping, as well as an additional 29 bottles. By the end of the day, 28 more bottles were added to this shipment. How many bottles were marked for shipping in total?

Gemini-1.5 Flash:

Here's how to break down the problem:

1. **Bottles sent to the first warehouse:** 100 bottles/hour * 1/2 = 50 bottles
2. **Bottles marked for shipping at the second location (triple the first warehouse):** 50 bottles * 3 = 150 bottles
3. **Additional bottles at the second location:** 150 bottles + 29 bottles = 179 bottles
4. **Total bottles marked for shipping:** 179 bottles + 28 bottles = 207 bottles

### Answer: 207 

Expected answer: 207

Correct? Yes

πŸ”— Follow-up

Problem: From the same factory scenario as before, reconsider the situation such that instead of adding 28 more bottles for shipment by the end of the day, they actually added 50 more bottles. How many bottles were marked for shipping in total now?

Gemini-1.5 Flash:

Here's the breakdown:

1. **Bottles sent to the first warehouse:** 100 bottles/hour * 1/2 = 50 bottles
2. **Bottles marked for shipping at the second location (triple the first warehouse):** 50 bottles * 3 = 150 bottles
3. **Additional bottles at the second location:** 150 bottles + 29 bottles = 179 bottles
4. **Total bottles marked for shipping:** 179 bottles + 50 bottles = 229 bottles

### Answer: 229 

Expected answer: 229

Correct? Yes

πŸ”— Problem

Problem: The height of a window frame is calculated as the sum of 925 divided by 37 and 26 inches. The width of the window is 11 inches greater than the height. The circumference of the window is calculated as the sum of twice the width and the height. Finally the size of the glass for the window is calculated by subtracting 32 from the circumference. Find the size of the glass required for the window?

Gemini-1.5 Flash:

Here's how to break down the problem step-by-step:

1. **Calculate the height of the window frame:**
   - 925 divided by 37 is 925 / 37 = 25 inches
   - The height of the frame is 25 inches + 26 inches = 51 inches

2. **Calculate the width of the window:**
   - The width is 11 inches greater than the height, so it's 51 inches + 11 inches = 62 inches

3. **Calculate the circumference of the window:**
   - The circumference is twice the width plus the height: (2 * 62 inches) + 51 inches = 175 inches

4. **Calculate the size of the glass:**
   - Subtract 32 inches from the circumference: 175 inches - 32 inches = 143 inches

### Answer: 143 

Expected answer: 143

Correct? Yes

πŸ”— Follow-up

Problem: Suppose that there was an error in the original measurements. The height of the window frame is instead calculated as the sum of 925 divided by 37 and 16 inches, not 26 inches. Recalculating with these new measurements, what would be the size of the glass required for the window now?

Gemini-1.5 Flash:

Let's recalculate with the corrected height:

1. **Calculate the height of the window frame:**
   - 925 divided by 37 is 925 / 37 = 25 inches
   - The height of the frame is 25 inches + 16 inches = 41 inches

2. **Calculate the width of the window:**
   - The width is 11 inches greater than the height, so it's 41 inches + 11 inches = 52 inches

3. **Calculate the circumference of the window:**
   - The circumference is twice the width plus the height: (2 * 52 inches) + 41 inches = 145 inches

4. **Calculate the size of the glass:**
   - Subtract 32 inches from the circumference: 145 inches - 32 inches = 113 inches

### Answer: 113 

Expected answer: 113

Correct? Yes

πŸ”— Problem

Problem: A pirate finds treasure with 135 gold coins. He divides these amongst his crew of 9. On another island, they find 323 emeralds which he divides amongst his crew of 19. He then multiplies these two shares to find out the total share per crew member. However, due to a miscount, he later realizes he has overcounted the share by 14. What is the corrected total share per crew member?

Gemini-1.5 Flash:

Here's how to solve this problem step-by-step:

1. **Gold coins per crew member:** The pirate divides 135 gold coins amongst 9 crew members, giving each crew member 135 / 9 = 15 gold coins.

2. **Emeralds per crew member:** On the other island, he divides 323 emeralds amongst 19 crew members, giving each crew member 323 / 19 = 17 emeralds.

3. **Initial total share:** He multiplies the gold and emerald shares to get a total share of 15 * 17 = 255.

4. **Corrected total share:** He overcounted the share by 14, so the corrected total share per crew member is 255 - 14 = 241.

### Answer: 241 

Expected answer: 241

Correct? Yes

πŸ”— Problem

Problem: A chocolatier has decided to make small chocolate bars that weigh 176 grams each. To get the right size, he divides each bar into 8 pieces, which means each piece weighs a certain number of grams. He then decides to make a new batch of chocolate using a special recipe. This recipe calls for a total of 38 grams of cocoa, but subtraction the weight of one piece from the 176g bars, plus an additional 26 grams of sugar. Simultaneously, the chocolatier decides to create another batch of chocolates that needs a total of 38 grams of cocoa and 18 grams of milk. What is the difference in the total weight of ingredients between the second and third batch of chocolates?

Gemini-1.5 Flash:

Here's how we can solve this problem step-by-step:

1. **Calculate the weight of one piece:** The chocolatier divides each 176-gram bar into 8 pieces, so each piece weighs 176 grams / 8 pieces = 22 grams.

2. **Calculate the total weight of the special recipe:** The special recipe uses 38 grams of cocoa minus the weight of one piece (22 grams) plus 26 grams of sugar, for a total of 38 - 22 + 26 = 42 grams.

3. **Calculate the total weight of the third batch:** The third batch uses 38 grams of cocoa and 18 grams of milk for a total of 38 + 18 = 56 grams.

4. **Find the difference in weight:** The difference between the special recipe (42 grams) and the third batch (56 grams) is 56 - 42 = 14 grams.

### Answer: 14 

Expected answer: 14

Correct? Yes

πŸ”— Follow-up

Problem: Continuing from the original problem, the chocolatier decides to reduce the amount of sugar in his special recipe. Initially, he was adding 26 grams of sugar but now, he's decided to only add 6 grams. How does this change in sugar affect the difference in the total weight of ingredients between the second (now modified) and third batch of chocolates?

Gemini-1.5 Flash:

Here's how the change in sugar affects the difference in weight:

1. **Calculate the new total weight of the special recipe:** With the reduced sugar, the special recipe now uses 38 grams of cocoa - 22 grams (one piece) + 6 grams of sugar = 22 grams.

2. **Calculate the new difference in weight:** The difference between the modified special recipe (22 grams) and the third batch (56 grams) is 56 - 22 = 34 grams.

3. **Compare the differences:** The original difference was 14 grams, and the new difference is 34 grams. The change in sugar increased the difference in weight by 34 - 14 = 20 grams.

### Answer: The difference in the total weight of ingredients between the second and third batch of chocolates increased by 20 grams. 

Expected answer: 34

Correct? No

πŸ”— Problem

Problem: Jenny has 9 red colored pencils in her art box. She also has some green colored pencils which amounts to 38 minus the number of red colored pencils she has. The total number of times she used all the pencils is the product of the number of green and red pencils she has. How many times did she use all her pencils?

Gemini-1.5 Flash:

Reasoning: Jenny has 38 - 9 = <<38-9=29>> 29 green colored pencils.
The product of the number of green and red pencils is 29 x 9 = <<29*9=261>>261.
### Answer: 261 

Expected answer: 261

Correct? Yes

πŸ”— Follow-up

Problem: Following from the previous scenario, Jenny also used her blue colored pencils an equivalent number of times to the sum of 31 and 16. Now, the total number of times she used all her pencils is equivalent to the times she used her blue pencils added to the times she used her green and red pencils. How many times in total did she use all her pencils?

Gemini-1.5 Flash:

Reasoning: Jenny used her blue pencils 31 + 16 = <<31+16=47>> 47 times.
In total, Jenny used all her pencils 47 + 261 = <<47+261=308>> 308 times.

### Answer: 308 

Expected answer: 308

Correct? Yes

πŸ”— Follow-up

Problem: Now, instead of having only 9 red colored pencils, Jenny actually had 12 of them. She again has green colored pencils which, as before, total 38 minus the number of red colored pencils. The total number of times she used all the pencils is the product of the number of green and red pencils she has, just as in the previous case. Now, with this change, how many times did she use all her pencils?

Gemini-1.5 Flash:

Reasoning: Jenny now has 38 - 12 = <<38-12=26>> 26 green colored pencils.
The product of the number of green and red pencils is 26 x 12 = <<26*12=312>>312.
### Answer: 312 

Expected answer: 312

Correct? Yes

πŸ”— Problem

Problem: A factory has just released a new robot model, where each model has 17 transistors and each transistor may have 16 separate connections. One of the newly manufactured robots by accident was made with one less connection than standard. However, to compensate for the mistake, an extra 41 connections were added elsewhere. What is the total number of connections in the strangely built robot?

Gemini-1.5 Flash:

Reasoning: A standard robot has 17 transistors * 16 connections/transistor = 272 connections.
The strangely built robot has 272 - 1 + 41 = 312 connections.
### Answer: 312 

Expected answer: 312

Correct? Yes

πŸ”— Follow-up

Problem: In the assembly line, another robot was produced similar to the first. However, this time instead of adding an additional 41 connections to compensate for the one lost, the production team decided to add only 13 additional connections. How many connections does this robot have now?

Gemini-1.5 Flash:

Reasoning: The robot starts with 272 connections - 1 connection = 271 connections.
With the additional 13 connections, the robot has 271 + 13 = 284 connections. 
### Answer: 284 

Expected answer: 284

Correct? Yes

πŸ”— Problem

Problem: At the local jungle gym, during busy hours, there are usually 24 kids climbing on each of the 31 different attractions. One rainy day, however, there were only 6 kids in total! If you subtract the number of kids on the rainy day from the usual busy day, and then further subtract 12 (the number of squirrels scampering around), how many kids will you have counted in total?

Gemini-1.5 Flash:

Reasoning: Usually, there are 24 kids * 31 attractions = 744 kids.
Subtracting the 6 kids on the rainy day, we have 744 - 6 = 738 kids.
Finally, subtracting the squirrels, we have 738 - 12 = 726 kids.
### Answer: 726 

Expected answer: 726

Correct? Yes

πŸ”— Follow-up

Problem: In the previous problem, instead of 31 attractions at the jungle gym, let's say there were only 6 attractions. So now, on a busy day, you have 24 kids at each of these 6 attractions. If that rainy day still only had 6 kids at the jungle gym in total, and there were 12 squirrels, how many kids will you have counted in total now?

Gemini-1.5 Flash:

Reasoning:  On a busy day, there would be 24 kids * 6 attractions = 144 kids. 
Subtracting the 6 kids on the rainy day, we have 144 - 6 = 138 kids.
Finally, subtracting the squirrels, we have 138 - 12 = 126 kids.
### Answer: 126 

Expected answer: 126

Correct? Yes

πŸ”— Problem

Problem: There's this mystical ring that, after you perform a special chant, it will grant you powers based on a complex magic formula. If the first step of the magical formula is subtracting 5 from 23 and then multiplying by the number of magical chants you perform, which in this case is 6. After that, the result is multiplied by 7 and again by 1. However, for the final step, you subtract 48 from the result. If you follow these steps, how powerful will the ring's magic be?

Gemini-1.5 Flash:

Here's how to break down the magic formula:

1. **Subtract 5 from 23:** 23 - 5 = 18
2. **Multiply by the number of chants (6):** 18 * 6 = 108
3. **Multiply by 7:** 108 * 7 = 756
4. **Multiply by 1:** 756 * 1 = 756
5. **Subtract 48:** 756 - 48 = 708

### Answer: 708 

Expected answer: 708

Correct? Yes

πŸ”— Follow-up

Problem: Imagine in the initial mystical chant, instead of subtracting 5 from 23, you subtracted 5 from just 8, then continued with the rest of the magic formula exactly the same - multiplying by the number of chants and so forth. How would this adjustment impact the final power of the ring?

Gemini-1.5 Flash:

Let's recalculate the magic formula with the change:

1. **Subtract 5 from 8:** 8 - 5 = 3
2. **Multiply by the number of chants (6):** 3 * 6 = 18
3. **Multiply by 7:** 18 * 7 = 126
4. **Multiply by 1:** 126 * 1 = 126
5. **Subtract 48:** 126 - 48 = 78

Comparing this to the original result of 708, the final power of the ring would be **lower** by 708 - 78 = 630.

### Answer: The ring's power would be 630 less powerful. 

Expected answer: 78

Correct? No

πŸ”— Problem

Problem: A child can make 15 cookies in one hour. If the child spends 24 hours making the cookies, how many cookies are made in total?

Gemini-1.5 Flash:

Reasoning: If the child makes 15 cookies in one hour, then in 24 hours, they would make 24*15 = <<24*15=360>> cookies. 

### Answer: 360 

Expected answer: 360

Correct? Yes

πŸ”— Follow-up

Problem: If the same child decides to increase their cookie production rate and can now make 40 cookies in one hour, how many cookies are made when they spend the same amount of time (24 hours) baking?

Gemini-1.5 Flash:

Reasoning: If the child now makes 40 cookies in one hour, then in 24 hours they would make 24 * 40 = <<24*40=960>> cookies.

### Answer: 960 

Expected answer: 960

Correct? Yes

πŸ”— Problem

Problem: A silversmith has 16 silver rings in stock. He decided to create more rings and ended up with 28 silver and 24 gold rings. Then he subtracted from them the number of his original stock of silver rings. He traded some rings and ended up with 21 rings less than what he had after the creation stage. After that, for a special order, he created 26 times the number of rings he had left. In addition, he had made 7 platinum and 47 bronze rings for another order. How many rings does the silversmith have in total now?

Gemini-1.5 Flash:

Here's how we can break down the problem step-by-step:

1. **Rings after creation:** The silversmith had 28 silver + 24 gold = 52 rings after creation.
2. **Rings after subtracting original stock:** After subtracting his original 16 silver rings, he had 52 - 16 = 36 rings.
3. **Rings after trading:** He traded some and had 36 - 21 = 15 rings left.
4. **Rings after special order:** He created 26 * 15 = 390 rings for the special order.
5. **Total rings:** He now has 390 + 15 + 7 platinum + 47 bronze = 459 rings.

### Answer: 459 

Expected answer: 444

Correct? No

πŸ”— Problem

Problem: A gardener plants flowers in several rows. Each row contains 40 flowers, but due to the rough soil conditions only half of them grow properly. In total, 19 rows are planted this way. Additionally, the gardener plants another small batch of 18 bulbs in one corner and 48 in another corner of the garden. What is the difference between the total number of flowers in the rows and the small corners?

Gemini-1.5 Flash:

Reasoning: 
1. In each row, 40/2 = 20 flowers grow properly.
2. There are 19 rows with 20 flowers each, so there are 19 * 20 = 380 flowers in total.
3. The gardener planted 18 + 48 = 66 flowers in the corners.
4. The difference between the flowers in rows and corners is 380 - 66 = 314.

### Answer: 314

Expected answer: 314

Correct? Yes

πŸ”— Problem

Problem: In the forest, a certain bird lays an average of 11 eggs per month. This month, the bird laid 4 times the average. Due to extreme weather conditions, the forest welcoming committee distributed an additional 40 eggs to various nests to support the bird population. How many eggs are there in the forest this month?

Gemini-1.5 Flash:

Reasoning: The bird laid 11*4 = <<11*4=44>>44 eggs this month.
There are 44+40 = <<44+40=84>>84 eggs in the forest this month.
### Answer: 84

Expected answer: 84

Correct? Yes

πŸ”— Follow-up

Problem: After examining the ground for fallen eggs, the forest rangers found more eggs which they distributed to the nests. They found 216 eggs in total, and divided them between 18 nests, before adding them to the initial number of eggs in the forest. How many eggs are there in the forest now?

Gemini-1.5 Flash:

Reasoning: Each nest received 216/18 = <<216/18=12>>12 eggs.
The total number of eggs in the forest is now 84+216 = <<84+216=300>>300 eggs.
### Answer: 300 

Expected answer: 96

Correct? No

πŸ”— Problem

Problem: You are mixing paints to create different shades. In one mixture, you have 41 drops of red paint. You then add 13 drops of white paint and the same amount of red paint as before. You take a sample of this mixture, which is 34 drops, and add that to a new mixture. Then take away the same amount of the 34 drop sample that you took originally. How many drops of paint are there in the new mixture?

Gemini-1.5 Flash:

Here's how we can break down the problem:

1. **Initial mixture:** You start with 41 drops of red paint and add 13 drops of white paint, giving you a total of 41 + 13 = 54 drops.
2. **Adding more red paint:** You then add another 41 drops of red paint, bringing the total to 54 + 41 = 95 drops.
3. **Adding a sample:** You take a 34 drop sample of the mixture and add it to a new mixture.
4. **Removing the sample:** You then remove the same amount (34 drops) from the new mixture.

Since you add the sample and then remove the same amount, the net change in the new mixture is zero. 

**Therefore, the number of drops of paint in the new mixture is the same as the amount you originally took out, which is 34 drops.**

### Answer: 34 

Expected answer: 95

Correct? No

πŸ”— Problem

Problem: A small toy car factory made 32 toy cars on Monday, but only 27 on Tuesday. They multiply the difference by 49 to determine their weekly goal. The staff number in the factory is 12, and every staff member makes 9 toy cars a day. They add 45 to the total number of toy cars prepared by staff members. On Friday, they prepare 31 additional toy cars and add this to the weekly goal and staff prepared cars. How many toy cars in total were made in this process?

Gemini-1.5 Flash:

Here's how to break down the problem step-by-step:

1. **Difference in production:**  The factory made 32 - 27 = 5 fewer toy cars on Tuesday.
2. **Weekly goal:** They multiply the difference by 49: 5 * 49 = 245.
3. **Staff production per day:** Each of the 12 staff members makes 9 toy cars a day, so they make a total of 12 * 9 = 108 toy cars per day.
4. **Total staff production for the week:** Assuming a 5-day workweek, the staff makes 108 * 5 = 540 toy cars.
5. **Adding to staff production:** They add 45 to the staff's total: 540 + 45 = 585.
6. **Friday's production:**  They add the 31 toy cars made on Friday: 585 + 31 = 616.
7. **Final total:** To get the total number of toy cars made, we add Friday's production to the weekly goal: 616 + 245 = 861.

### Answer: 861 

Expected answer: 429

Correct? No

πŸ”— Problem

Problem: A farmer harvested 45 carrots in one day from his farm. He noticed that for every carrot over 44 per day, he can earn 29 dollars. How much would the farmer have earned if this continued?

Gemini-1.5 Flash:

Reasoning: The farmer harvested 45-44 = 1 carrot over 44.
The farmer earned 1*29 = 29 dollars.
### Answer: 29 

Expected answer: 29

Correct? Yes

πŸ”— Follow-up

Problem: Continuing from our previous scenario, let's suppose that the market rate for extra carrots has now changed. Now, for every carrot that the farmer harvests over 44 per day, he can earn 41 dollars instead of 29. How much would his new earnings be if he still harvested 45 carrots in one day?

Gemini-1.5 Flash:

Reasoning: The farmer still harvested 45-44 = 1 carrot over 44.
The farmer's earnings are now 1*41 = 41 dollars.
### Answer: 41 

Expected answer: 41

Correct? Yes

πŸ”— Problem

Problem: In a sock factory, a worker started with 26 pairs of socks. Unfortunately, 50 pairs got torn and had to be discarded. The worker was able to produce 36 more pairs to replace them. Each pair of socks is sold for $37. After earning from the sock sales, the worker found a $13 bill on the floor. How much money does the worker have in total?

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Start with the initial pairs:** The worker began with 26 pairs of socks.
2. **Subtract the torn pairs:** 26 - 50 = -24. This means the worker is actually short 24 pairs of socks.
3. **Add the new pairs:** -24 + 36 = 12. The worker now has 12 pairs of socks after replacing the torn ones.
4. **Calculate the total earnings:** 12 pairs * $37/pair = $444
5. **Add the found money:** $444 + $13 = $457

### Answer: $457 

Expected answer: 457

Correct? Yes

πŸ”— Follow-up

Problem: In the sock factory situation previously described, let's suppose that instead of selling each pair of socks for $37, they instead sold each pair for $40. How much money does the worker have in total now?

Gemini-1.5 Flash:

Let's recalculate the earnings with the new price:

1. **Calculate the total earnings:** 12 pairs * $40/pair = $480
2. **Add the found money:** $480 + $13 = $493

### Answer: $493 

Expected answer: 493

Correct? Yes

πŸ”— Problem

Problem: A jewelry maker starts with 38 beads to make a bracelet. However, the number of beads was not right, so she removed a number of beads equal to dividing 560 by 40. However, she thinks her initial count may have been wrong and she may have actually started with 15 more beads than she initially thought. After adjusting the count and removing some beads, she adds one more bead, and then 39 more. How many beads does the jewelry maker have now?

Gemini-1.5 Flash:

Here's how to break down the problem step-by-step:

1. **Beads removed:** The jewelry maker removed 560 / 40 = 14 beads.

2. **Initial count correction:** She believes she may have started with 38 + 15 = 53 beads.

3. **Beads after removal:** After removing beads, she had 53 - 14 = 39 beads.

4. **Adding more beads:** She added 1 + 39 = 40 more beads.

5. **Total beads:** The jewelry maker now has 39 + 40 = 79 beads.

### Answer: 79 

Expected answer: 79

Correct? Yes

πŸ”— Follow-up

Problem: In the continuation of the previous story, the jewelry maker decided to make another adjustment after adding beads to her bracelet. She then removed again the same number of beads she removed earlier, equal to dividing 560 by 40. After that, she finds a small box with an additional 20 beads in it that she decides to add to the bracelet. How many beads does the jewelry maker have now on her bracelet?

Gemini-1.5 Flash:

Let's break down the steps:

1. **Beads removed:**  She removed 560 / 40 = 14 beads again.

2. **Beads after removal:** She had 79 - 14 = 65 beads.

3. **Adding the box of beads:** She added 20 more beads from the box.

4. **Total beads:** The jewelry maker now has 65 + 20 = 85 beads on her bracelet.

### Answer: 85 

Expected answer: 85

Correct? Yes

πŸ”— Follow-up

Problem: In a different scenario, suppose the jewelry maker initially had 50 beads instead of 38. She still removed a number of beads equal to 560 divided by 40. Afterwards, she realized she might have actually started with 15 more beads than she originally thought. After correcting her count and removing some beads, she added one more bead, and then 39 more beads. How many beads does the jewelry maker have now in this case?

Gemini-1.5 Flash:

Let's solve this step by step:

1. **Beads removed:**  The jewelry maker removed 560 / 40 = 14 beads.

2. **Initial count correction:** She believes she may have started with 50 + 15 = 65 beads.

3. **Beads after removal:** After removing beads, she had 65 - 14 = 51 beads.

4. **Adding more beads:** She added 1 + 39 = 40 more beads.

5. **Total beads:** The jewelry maker now has 51 + 40 = 91 beads.

### Answer: 91 

Expected answer: 91

Correct? Yes

πŸ”— Problem

Problem: In an aquarium, there are initially 30 sharks. But then, 23 of them are moved to a different area of the aquarium. A few days later, an additional 14 sharks are brought in, followed by 3 more being moved to the other area. The number of sharks is then multiplied by 43 for a research study. What is the final figure for the research?

Gemini-1.5 Flash:

Reasoning: After the first move, the aquarium has 30 - 23 = <<30-23=7>>7 sharks. 
After the second move, it has 7 + 14 = <<7+14=21>>21 sharks.
After the third move, it has 21 - 3 = <<21-3=18>>18 sharks.
Finally, for the research study, the number of sharks is multiplied by 43, resulting in 18 * 43 = <<18*43=774>>774.

### Answer: 774

Expected answer: 774

Correct? Yes

πŸ”— Follow-up

Problem: We are back at the aquarium again! Previously, we mentioned the number of sharks being multiplied by 43 for a research study. But this time, instead of multiplying by 43, the scientists made a mistake and only multiplied it by 4. What would the new figure for the experiment be?

Gemini-1.5 Flash:

Reasoning: Remember, after the third move, the aquarium had 18 sharks. The scientists mistakenly multiplied this number by 4, resulting in 18 * 4 = <<18*4=72>>72 sharks.

### Answer: 72 

Expected answer: 72

Correct? Yes

πŸ”— Problem

Problem: In a puzzle game, each round you collect 150 points which are then divided by 10 to determine the number of gold coins you earn. After two rounds, you earned some gold coins. In the third round, you collected 28 emeralds and 14 sapphires but you had to sacrifice the same amount of gold coins as you earned in the first two rounds. How many emeralds and sapphires did you have left after the third round?

Gemini-1.5 Flash:

Here's how we can solve this:

**Round 1 and 2:**

* **Points per round:** 150 points
* **Gold coins per round:** 150 points / 10 = 15 gold coins
* **Total gold coins earned in two rounds:** 15 coins/round * 2 rounds = 30 gold coins

**Round 3:**

* **Gold coins sacrificed:** 30 gold coins
* **Emeralds and sapphires:** 28 emeralds + 14 sapphires = 42 total

**After Round 3:**

* **Emeralds and Sapphires left:** Since you sacrificed gold coins, you still have **42 emeralds and sapphires** left.

**Important Note:**  The problem doesn't specify that the emeralds and sapphires have any relationship to the gold coins. It's likely a trick to mislead you.

### Answer: 42 

Expected answer: 12

Correct? No

πŸ”— Problem

Problem: A train gets to carry 15 containers every day. On Fridays, the train gets to carry an extra 12 containers than usual. The following Monday, the train carries an additional 26 containers. However, on Wednesday, the load decreases by 32 containers. For a particular trip, the train is coupled with 2 more containers, and after it makes one stop, an additional 48 containers are loaded onto the train. How many containers is the train carrying at this point?

Gemini-1.5 Flash:

Here's how we can solve this problem step by step:

1. **Friday's Load:** The train carries 15 + 12 = 27 containers on Fridays.

2. **Monday's Load:** The train carries 27 + 26 = 53 containers on Mondays.

3. **Wednesday's Load:** The train carries 53 - 32 = 21 containers on Wednesdays.

4. **Coupled Containers:** The train now has 21 + 2 = 23 containers.

5. **Additional Load:** After the stop, the train carries 23 + 48 = 71 containers.

### Answer: 71 

Expected answer: 71

Correct? Yes

πŸ”— Problem

Problem: A lemon farmer had harvested 39 lemons in the morning and 33 in the afternoon. Unfortunately, 12 lemons got spoiled by the end of the day. The next day, the farmer used 23 lemons to make lemonade. How many lemons did he have left after making the lemonade?

Gemini-1.5 Flash:

Reasoning: The farmer harvested 39+33 = 72 lemons in total.
After the spoiled lemons, the farmer had 72-12 = 60 lemons left.
After making lemonade, the farmer had 60-23 = 37 lemons left.
### Answer: 37 

Expected answer: 37

Correct? Yes

πŸ”— Follow-up

Problem: In our previous calculations, we found out how many lemons the farmer had left after some got spoiled and some were used to make lemonade. However, what if the farmer actually had 24 lemons get spoiled on the first day instead of 12? How many lemons would the farmer have left after making the lemonade?

Gemini-1.5 Flash:

Reasoning: The farmer harvested 39 + 33 = 72 lemons in total.
After the spoiled lemons, the farmer had 72 - 24 = 48 lemons left.
After making lemonade, the farmer had 48 - 23 = 25 lemons left.
### Answer: 25 

Expected answer: 25

Correct? Yes

πŸ”— Problem

Problem: A bee lands on 33 flowers in an hour. If the bee is collecting 15 nectar droplets from each flower, how many nectar droplets does it have after an hour if it started with 26 nectar droplets?

Gemini-1.5 Flash:

Reasoning: The bee collects 33 flowers * 15 nectar droplets/flower = <<33*15=495>> 495 nectar droplets in an hour.
The bee has a total of 495 nectar droplets + 26 nectar droplets = <<495+26=521>> 521 nectar droplets.
### Answer: 521 

Expected answer: 521

Correct? Yes

πŸ”— Follow-up

Problem: If instead of starting with 26 nectar droplets, the bee had initially found 49 nectar droplets before it started its hour of flower visits, how many nectar droplets would the bee have after an hour of collecting nectar from 33 flowers with 15 nectar droplets each?

Gemini-1.5 Flash:

Reasoning: The bee collects 33 flowers * 15 nectar droplets/flower = <<33*15=495>> 495 nectar droplets in an hour.
The bee has a total of 495 nectar droplets + 49 nectar droplets = <<495+49=544>> 544 nectar droplets. 
### Answer: 544 

Expected answer: 544

Correct? Yes

πŸ”— Problem

Problem: A company produces 36 marshmallow packs in an hour. To meet a sudden increase in demand, they decide to increase their production. They add an extra 350 marshmallows to their daily production, which is distributed evenly over 7 hours of their working day. Additionally, they add another 6 marshmallow packs to their hourly production. But, due to some limitations, they end up producing 43 less packs per hour than their goal. How many marshmallow packs per hour are they now producing?

Gemini-1.5 Flash:

Here's how to break down the problem step by step:

1. **Extra marshmallows per hour:** They add 350 marshmallows to their daily production, distributed over 7 hours, so they add 350/7 = 50 marshmallows per hour.

2. **Total extra production per hour:** This includes the extra marshmallows and the 6 additional packs: 50 marshmallows + (6 packs * marshmallows per pack) = 50 + 6*x, where x is the number of marshmallows per pack.

3. **Goal production per hour:** Their original production was 36 packs per hour, and they aim to add 6 more: 36 + 6 = 42 packs per hour.

4. **Actual production per hour:** They produce 43 less than their goal: 42 - 43 = -1 packs per hour. This means they are producing less than their original production.

5. **Combined production:** Their actual production is the original production plus the extra production: 36 + (50 + 6*x) -1 = 36 + 50 + 6*x -1 = 85 + 6*x

6. **Since they are producing less than their original production, this means their actual production is less than 36:** 85 + 6*x < 36

7. **Solving for x:** Subtract 85 from both sides: 6*x < -49
8. **Divide both sides by 6:** x < -8.17

9. **This result doesn't make sense** because we can't have a negative number of marshmallows per pack. This indicates there's an error in the problem statement, likely the number of less packs produced per hour. 

**Without a corrected number of less packs produced per hour, we can't determine the exact number of marshmallow packs they are now producing.** 

Expected answer: 49

Correct? No

πŸ”— Problem

Problem: A wizard casts a spell that produces 882 glimmering lights over a span of 21 days. That's an average of how many lights a day? In comparison, another wizard casts a spell that produces 460 glowing orbs in 20 days. What is the daily average here? Now, let's assume that the difference in their daily averages times the second wizard's daily average is a magical constant represented by 'n'. Can you find out what 'n' is?

Gemini-1.5 Flash:

Here's how we can solve this step-by-step:

**Step 1: Find the average lights per day for the first wizard.**

* Divide the total number of lights by the number of days: 882 lights / 21 days = 42 lights/day

**Step 2: Find the average orbs per day for the second wizard.**

* Divide the total number of orbs by the number of days: 460 orbs / 20 days = 23 orbs/day

**Step 3: Calculate the difference in daily averages.**

* Subtract the second wizard's daily average from the first wizard's daily average: 42 lights/day - 23 orbs/day = 19

**Step 4: Calculate the magical constant 'n'.**

* Multiply the difference in daily averages by the second wizard's daily average: 19 * 23 = 437

### Answer: 437 

Expected answer: 437

Correct? Yes

πŸ”— Problem

Problem: A candy factory has 20 different flavors of candy. Their bestselling flavors are the Sugar Rush, which has 14 different base ingredients, the Candy Twirl, which has 25 base ingredients, and the Jawbreaker, which has 16 base ingredients. They create a Special Mix which combines all of these bestsellers and adds 43 extra goodies, including sprinkles and marshmallows. To create a limited edition candy, they take a piece of the Special Mix, add 7 uniquely crafted sweets, then combine this with one of each flavor from their 20 different flavored candies (excluding 19 of them so it's not too overwhelming). They then top it all off by removing 3 experimental sweets that didn't taste quite right. What is the count of various components used in creating this limited edition candy?

Gemini-1.5 Flash:

Here's how we can break down the components of the limited edition candy:

1. **Special Mix:**
   - Sugar Rush: 14 base ingredients
   - Candy Twirl: 25 base ingredients
   - Jawbreaker: 16 base ingredients
   - Extra goodies: 43
   - Total Special Mix components: 14 + 25 + 16 + 43 = <<14+25+16+43=98>> 98

2. **Limited Edition Additions:**
   - Uniquely crafted sweets: 7
   - One of each flavor (excluding 19): 20 - 19 = 1

3. **Final Adjustments:**
   - Removed experimental sweets: -3

4. **Total Components in Limited Edition Candy:**
   - Special Mix components: 98
   - Uniquely crafted sweets: 7
   - One of each flavor: 1
   - Removed experimental sweets: -3
   - Total: 98 + 7 + 1 - 3 = <<98+7+1-3=103>> 103

### Answer: 103 

Expected answer: 103

Correct? Yes

πŸ”— Follow-up

Problem: Further consider the candy factory's process. If instead of the Jawbreaker having 16 base ingredients, it had 23 base ingredients instead, then how many different components would be used in creating the same limited edition candy as before?

Gemini-1.5 Flash:

Let's adjust the Special Mix calculation based on the new Jawbreaker ingredient count:

1. **Special Mix:**
   - Sugar Rush: 14 base ingredients
   - Candy Twirl: 25 base ingredients
   - Jawbreaker: 23 base ingredients 
   - Extra goodies: 43
   - Total Special Mix components: 14 + 25 + 23 + 43 = <<14+25+23+43=105>> 105

2. The rest of the limited edition candy creation remains the same:

   - Uniquely crafted sweets: 7
   - One of each flavor (excluding 19): 20 - 19 = 1
   - Removed experimental sweets: -3

3. **Total Components in Limited Edition Candy:**
   - Special Mix components: 105
   - Uniquely crafted sweets: 7
   - One of each flavor: 1
   - Removed experimental sweets: -3
   - Total: 105 + 7 + 1 - 3 = <<105+7+1-3=109>> 109

### Answer: 109

Expected answer: 110

Correct? No

πŸ”— Problem

Problem: In a special operation, 32 police officers were assigned to the north district, 33 were sent to the south district, and 29 officers were held for the downtown district. After the operation, 21 officers from the downtown district were transferred elsewhere. A week later, on a different assignment, 39 officers were added to the remaining duty force. Later that day, another 14 officers joined the force. How many officers were on duty by the end of the day?

Gemini-1.5 Flash:

Here's how to break down the problem step-by-step:

1. **Start with the initial number of officers:** 32 (north) + 33 (south) + 29 (downtown) = 94 officers.

2. **Subtract the officers transferred from downtown:** 94 - 21 = 73 officers.

3. **Add the officers assigned on the new assignment:** 73 + 39 = 112 officers.

4. **Add the final group of officers:** 112 + 14 = 126 officers.

### Answer: 126 

Expected answer: 126

Correct? Yes

πŸ”— Follow-up

Problem: The previous problem had us determine the total number of police officers on duty under certain conditions. Now, let's imagine a slightly different scenario. Like the previous situation, there were still 32 officers assigned to the north district and 33 sent to the south. The number for the downtown district was also the same, at 29. However, this time around, only 21 officers from the total force were transferred elsewhere instead of the original scenario's subtraction. A week later, an additional 22 officers, fewer than the 39 from the original scenario, were brought in for a different assignment. That same day, another addition of 14 officers was made, just like with the initial series of events. New question: How many officers total were on duty by the end of the day in this amended scenario?

Gemini-1.5 Flash:

Here's the breakdown:

1. **Start with the initial number of officers:** 32 (north) + 33 (south) + 29 (downtown) = 94 officers.

2. **Subtract the officers transferred from the entire force (not just downtown):** 94 - 21 = 73 officers.

3. **Add the officers assigned on the new assignment:** 73 + 22 = 95 officers.

4. **Add the final group of officers:** 95 + 14 = 109 officers.

### Answer: 109 

Expected answer: 109

Correct? Yes

πŸ”— Problem

Problem: The distance between the Moon and the Earth changes throughout the month. On one particular day, the distance was 36 million kilometers but decreased by 19 million kilometers later in the month. Then it increased again by 11 million kilometers. If that distance, in millions of kilometers, times 19 minus 27 equals to a certain value, what is the value?

Gemini-1.5 Flash:

Reasoning: After the first decrease, the distance between the Moon and the Earth was 36 - 19 = 17 million kilometers.
Then, after the increase, the distance was 17 + 11 = 28 million kilometers.
Multiplying this distance by 19 gives us 28 * 19 = 532.
Finally, subtracting 27 from this value results in 532 - 27 = 505.

### Answer: 505

Expected answer: 505

Correct? Yes

πŸ”— Follow-up

Problem: In the scenario mentioned earlier about the distance between the Moon and the Earth: on one particular day, the distance was 36 million kilometers but decreased by 19 million kilometers later in the month. It further increased by 11 million kilometers. Previously we calculated that distance, in millions of kilometers, times 19 and subtracted 27. But what if, instead of subtracting 27, we were to subtract 45? What would be the new value of the total distance?

Gemini-1.5 Flash:

We already know that the final distance between the Moon and Earth is 28 million kilometers. 

We need to multiply this distance by 19, which gives us 28 * 19 = 532.

Then, instead of subtracting 27, we subtract 45, resulting in 532 - 45 = 487.

### Answer: 487 

Expected answer: 487

Correct? Yes

πŸ”— Problem

Problem: A tiger has an average step length of 9 meters. If a tiger took two steps and then leaped 44 meters, it would have covered a certain distance. Another tiger covered a distance combining 23 meters with a leap and a 46-meter run but then retraces the distance equal to the first tiger's steps and the leap. How much distance did the second tiger cover finally?

Gemini-1.5 Flash:

Here's how to break down the problem:

* **First Tiger's Distance:**
    * Two steps: 2 steps * 9 meters/step = 18 meters
    * Total distance: 18 meters + 44 meters = 62 meters

* **Second Tiger's Initial Distance:**
    * Total distance: 23 meters + 46 meters = 69 meters

* **Second Tiger's Retraced Distance:**
    * Retraced distance is the same as the first tiger's total distance: 62 meters

* **Second Tiger's Final Distance:**
    * Final distance: 69 meters - 62 meters = 7 meters

### Answer: 7 

Expected answer: 7

Correct? Yes

πŸ”— Follow-up

Problem: Continuing from the previous situation, after retracing the distance equal to the first tiger's steps and the leap, the second tiger then decides to run an additional 30 meters before making a 44-meter leap. How much total distance did the second tiger cover after all these movements?

Gemini-1.5 Flash:

Here's the breakdown:

* **Second Tiger's Initial Distance:** We know from the previous calculation that the second tiger covered 69 meters initially.
* **Second Tiger's Retraced Distance:**  This remains the same as before, 62 meters.
* **Second Tiger's Additional Run:** 30 meters
* **Second Tiger's Final Leap:** 44 meters

* **Total Distance:** 69 meters (initial) - 62 meters (retraced) + 30 meters (run) + 44 meters (leap) = 81 meters

### Answer: 81 

Expected answer: 81

Correct? Yes

πŸ”— Problem

Problem: A toothpaste factory produces 26 tubes of toothpaste every hour. On Sundays, they work for 7 hours and produce additional 8 tubes of toothpaste. So, in one Sunday, they produce ((26 * 7) + 8) tubes. The following Monday, they continue their production by adding another 31 tubes to their Sunday's total. In parallel, in the packaging department, they have 50 empty boxes. They use 19 of them for another department, leaving them with (50 - 19) boxes. The total number of toothpaste tubes ready is calculated by adding the packaged boxes number with Monday's production. On Tuesday, they produced an additional 48 tubes of toothpaste. What is the total number of produced toothpaste tubes until Tuesday, inclusive?

Gemini-1.5 Flash:

Here's how we can break down the problem step-by-step:

* **Sunday's Production:** (26 * 7) + 8 = 182 + 8 = 190 tubes
* **Monday's Production:** 190 + 31 = 221 tubes
* **Available Boxes:** 50 - 19 = 31 boxes
* **Total Tubes Ready After Monday:** 31 boxes (since each box can hold one tube)
* **Tuesday's Production:** 48 tubes

**Total Produced Tubes Until Tuesday:** 221 (Monday) + 48 (Tuesday) = 269 tubes

### Answer: 269 

Expected answer: 300

Correct? No

πŸ”— Problem

Problem: In a magical forest, a unicorn has 42 rainbow pebbles. A day later, it finds 26 more. It also has a stash of 44 dreamberries. Later on, the unicorn gathers 33 more rainbow pebbles and adds them with its stash of dreamberries. Finally, the unicorn finds 40 magical dandelions and adds them to his stash, but oh no, he loses 14! How many items does the unicorn have altogether after these events?

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Rainbow Pebbles:** The unicorn starts with 42 pebbles, finds 26 more, and then finds 33 more. That's a total of 42 + 26 + 33 = 101 rainbow pebbles.

2. **Dreamberries:** The unicorn keeps its original 44 dreamberries.

3. **Magical Dandelions:** The unicorn finds 40 magical dandelions but loses 14, leaving him with 40 - 14 = 26 dandelions.

4. **Total Items:** To find the total, add up the number of each type of item: 101 (rainbow pebbles) + 44 (dreamberries) + 26 (magical dandelions) = 171 items.

### Answer: 171 

Expected answer: 171

Correct? Yes

πŸ”— Follow-up

Problem: In the previous magical scenario, consider that instead of initially having 42 rainbow pebbles, the unicorn started with just 40. It still finds 26 more the following day. Maintaining his stash of 44 dreamberries, the unicorn still accumulates 33 more rainbow pebbles and adds them to the dreamberries. Once again, the unicorn ventures to obtain an additional 40 magical dandelions, but unfortunately, he loses 14. After these events, how many items does the unicorn have?

Gemini-1.5 Flash:

Here's the breakdown with the updated information:

1. **Rainbow Pebbles:** The unicorn starts with 40 pebbles and finds 26 more, totaling 40 + 26 = 66 rainbow pebbles.

2. **Dreamberries:** The unicorn maintains his stash of 44 dreamberries. 

3. **Additional Rainbow Pebbles:** The unicorn finds 33 more rainbow pebbles, adding to his total of 66 + 33 = 99 rainbow pebbles.

4. **Magical Dandelions:** The unicorn finds 40 magical dandelions but loses 14, leaving him with 40 - 14 = 26 dandelions.

5. **Total Items:**  The unicorn has 99 (rainbow pebbles) + 44 (dreamberries) + 26 (magical dandelions) = 169 items.

### Answer: 169 

Expected answer: 169

Correct? Yes

πŸ”— Problem

Problem: A pirate captain has a treasure chest containing 23 types of jewels. Each type has 28 jewels. Tired from his adventure, he mistakenly lost 40 jewels on his way back to his ship. The next day, he luckily found 16 jewels from a deserted island. How many jewels does he have now in his treasure chest?

Gemini-1.5 Flash:

Reasoning: The pirate captain had 23*28 = <<23*28=644>> 644 jewels in total.
He lost 40 jewels, leaving him with 644 - 40 = <<644-40=604>> 604 jewels.
He found 16 jewels, bringing his total to 604 + 16 = <<604+16=620>> 620 jewels.
### Answer: 620 

Expected answer: 620

Correct? Yes

πŸ”— Follow-up

Problem: Following the discovery of additional jewels, the pirate captain realized he had miscalculated the number of types of jewels in his original stash. Instead of 23 types of jewels, he remembered that he actually only had 17 types originally, with each type still containing 28 jewels. After recalculating his treasure and still taking into account the loss of 40 jewels and the 16 he found on a deserted island, how many jewels does he have now?

Gemini-1.5 Flash:

Reasoning: The pirate captain originally had 17 * 28 = <<17*28=476>> 476 jewels.
After losing 40 jewels, he had 476 - 40 = <<476-40=436>> 436 jewels.
After finding 16 jewels, he has 436 + 16 = <<436+16=452>> 452 jewels.
### Answer: 452 

Expected answer: 452

Correct? Yes

πŸ”— Problem

Problem: In a distant galaxy, a star shines brightly with 38 neutrons. It then gains 4 more. This total number gets multiplied by 18 to create a sensational energy output. During an explosion, it additionally releases the energy equivalent to 6 plus 25. How much total energy does the star emit?

Gemini-1.5 Flash:

Here's how to break down the problem step-by-step:

1. **Start with the initial neutrons:** The star begins with 38 neutrons.
2. **Add the gained neutrons:** It gains 4 more, bringing the total to 38 + 4 = 42 neutrons.
3. **Multiply by 18:** The energy output is 42 * 18 = 756.
4. **Explosion energy:** The explosion releases 6 + 25 = 31 energy units.
5. **Total energy:**  The total energy emitted is 756 + 31 = 787.

### Answer: 787 

Expected answer: 787

Correct? Yes

πŸ”— Follow-up

Problem: Now consider instead that the star had only 38 neutrons initially, and then it gains only 4 more. This total number is then multiplied by 10, for a lower energy output. During an explosion, it still releases additional energy equivalent to 6 plus 25. Now, how much total energy does the star emit?

Gemini-1.5 Flash:

Let's break down the problem step-by-step:

1. **Start with the initial neutrons:** The star begins with 38 neutrons.
2. **Add the gained neutrons:** It gains 4 more, bringing the total to 38 + 4 = 42 neutrons.
3. **Multiply by 10:** The energy output is 42 * 10 = 420.
4. **Explosion energy:** The explosion releases 6 + 25 = 31 energy units.
5. **Total energy:**  The total energy emitted is 420 + 31 = 451.

### Answer: 451 

Expected answer: 451

Correct? Yes

πŸ”— Problem

Problem: A gardener planted 13 Sunflowers in his garden. The next day, he worked out that he needed to plant more, with the number being calculated as 37 times the number of petals on one sunflower, which is 5, minus 18. On the following day, he subtracted 10 flowers from that number, then added his initial sunflowers back, creating a new total. Meanwhile, he figured out that in a special part of his garden, ideal for 92 orchids he had, each spot can hold 23, so he calculated how many spots needed. By the end of the week, he summed up the total number of plants he worked on and the spots needed, then he doubled that total for no particular reason. How many did he end up with?

Gemini-1.5 Flash:

Here's how we can break down the problem step-by-step:

* **Step 1: Flowers planted the second day:** 
   - 37 times the number of petals (5) is 37 * 5 = 185
   - Minus 18 gives us 185 - 18 = 167 sunflowers
* **Step 2: Flowers after the third day:**
   - Subtracting 10 from the previous day's total gives 167 - 10 = 157 sunflowers
   - Adding the initial 13 sunflowers gives 157 + 13 = 170 sunflowers
* **Step 3: Orchid spots:**
   - 92 orchids divided by 23 spots per orchid gives 92 / 23 = 4 spots
* **Step 4: Total plants and spots:**
   - Summing the sunflowers and orchid spots gives 170 + 4 = 174
* **Step 5: Doubling the total:**
   - Doubling the total gives 174 * 2 = 348

### Answer: 348 

Expected answer: 348

Correct? Yes

πŸ”— Follow-up

Problem: After all of his calculations and planting, the gardener discovered an error in his original calculations: instead of 37 times the number of petals on one sunflower, which is 5, it should have been 47 times the number of petals on one sunflower, minus 18. He corrected this mistake in his calculations, following the same steps as before, then doubled that total for no particular reason. How many did he end up with by using this new calculation?

Gemini-1.5 Flash:

Let's retrace the gardener's steps with the corrected calculation:

* **Step 1: Flowers planted the second day (corrected):**
    - 47 times the number of petals (5) is 47 * 5 = 235
    - Minus 18 gives us 235 - 18 = 217 sunflowers
* **Step 2: Flowers after the third day (corrected):**
    - Subtracting 10 from the previous day's total gives 217 - 10 = 207 sunflowers
    - Adding the initial 13 sunflowers gives 207 + 13 = 220 sunflowers
* **Step 3: Orchid spots (unchanged):**
    - 92 orchids divided by 23 spots per orchid gives 92 / 23 = 4 spots
* **Step 4: Total plants and spots (corrected):**
    - Summing the sunflowers and orchid spots gives 220 + 4 = 224
* **Step 5: Doubling the total (corrected):**
    - Doubling the total gives 224 * 2 = 448

### Answer: 448 

Expected answer: 448

Correct? Yes

πŸ”— Problem

Problem: In a particular pond, there are 18 frogs. Each frog can catch 21 flies in a day. How many flies do all the frogs catch in a day?

Gemini-1.5 Flash:

Reasoning: If each of the 18 frogs catches 21 flies, then all the frogs together catch 18*21 = <<18*21=378>>378 flies in a day. 
### Answer: 378 

Expected answer: 378

Correct? Yes

πŸ”— Follow-up

Problem: Using the initial information from the previous problem where 18 frogs catch 21 flies each in a day (resulting in a total of 'j' flies), imagine the scenario where a particularly voracious toad comes by the next day and catches an additional 39 flies. How many flies have been caught in total over the two days then?

Gemini-1.5 Flash:

Reasoning: We know that the frogs caught 378 flies in a day, which we denoted as 'j'. 
Adding the toad's catch of 39 flies to the frogs' catch gives us a total of 378 + 39 = 417 flies caught over the two days.
### Answer: 417 

Expected answer: 417

Correct? Yes

πŸ”— Follow-up

Problem: Using the information from the previous problem, now consider if the number of frogs in the pond increased to 46. If each frog can still catch 21 flies in a day, how many flies do all the frogs catch in a day now?

Gemini-1.5 Flash:

Reasoning: If there are now 46 frogs, and each catches 21 flies, then they catch a total of 46*21 = <<46*21=966>> 966 flies in a day. 
### Answer: 966 

Expected answer: 966

Correct? Yes

πŸ”— Problem

Problem: A community center has 21 chairs in their main meeting room. They are supplemented with an additional 22 chairs from the storage room for a large event. How many chairs are in the meeting room now for the event?

Gemini-1.5 Flash:

The community center now has 21 + 22 = 43 chairs in the meeting room. 
### Answer: 43 

Expected answer: 43

Correct? Yes

πŸ”— Follow-up

Problem: Now, instead of starting with 21 chairs in the main meeting room at the community center, suppose they had only 12 chairs. They still supplement with an additional 22 chairs from the storage room for the event. How many chairs are in the meeting room now for the event?

Gemini-1.5 Flash:

If they start with 12 chairs, they now have 12 + 22 = 34 chairs in the meeting room.
### Answer: 34 

Expected answer: 34

Correct? Yes

πŸ”— Problem

Problem: There are 14 elephants in a conservation park. This year, 11 new baby elephants were born, and the park received 25 more elephants from various rescues. How many elephants are there in the park now?

Gemini-1.5 Flash:

Reasoning: The park started with 14 elephants and gained 11 new babies, bringing the total to 14+11 = <<14+11=25>>25 elephants.
Then, the park received 25 more elephants, increasing the total to 25+25 = <<25+25=50>>50 elephants.
### Answer: 50 

Expected answer: 50

Correct? Yes

πŸ”— Follow-up

Problem: Unfortunately, due to unfortunate circumstances, 27 elephants had to be relocated to different parks over the course of the year. How many elephants are left in the park now?

Gemini-1.5 Flash:

Reasoning: The park had 50 elephants and then 27 were relocated, leaving 50-27 = <<50-27=23>>23 elephants.
### Answer: 23 

Expected answer: 23

Correct? Yes

πŸ”— Follow-up

Problem: Suppose initially, there were 38 elephants in the conservation park instead of 14. If the park still received 11 new baby elephants and 25 more elephants from various rescues this year, how many elephants would there be in the park now?

Gemini-1.5 Flash:

Reasoning: The park started with 38 elephants, gained 11 new babies, bringing the total to 38 + 11 = <<38+11=49>> 49 elephants.
Then, the park received 25 more elephants, increasing the total to 49 + 25 = <<49+25=74>> 74 elephants.
### Answer: 74 

Expected answer: 74

Correct? Yes

πŸ”— Problem

Problem: A treasure chest contains 23 emeralds and 30 diamonds. Unfortunately, 39 of the stones are fake and had to be removed. The number of real stones left (y) is multiplied by itself and then 37 is subtracted to get a number (g) that represents the value of the chest. In another chest, there were 540 rubies which have been equally shared amongst 45 pirates, and then 3 are lost in the division. The remaining number (x) is subtracted from the value of the first chest (g) to get a new value. In the same chest as the rubies, there were also 23 pearls and 11 zirconias, but 9 pieces had to be discarded due to damage. The count (s) is subtracted from the new value to determine the value (m) of the remaining treasure. What is the value (m) of the remaining treasure?

Gemini-1.5 Flash:

Let's break down the problem step by step:

1. **Real Stones in the First Chest:**
   - There are 23 emeralds + 30 diamonds = 53 stones in total.
   - Since 39 are fake, there are 53 - 39 = 14 real stones left (y).

2. **Value of the First Chest (g):**
   - The value is calculated as (y * y) - 37.
   - Substituting y = 14, we get (14 * 14) - 37 = 196 - 37 = 159.

3. **Rubies Remaining (x):**
   - 540 rubies divided equally among 45 pirates gives 540 / 45 = 12 rubies per pirate.
   - After losing 3 rubies, there are 12 - 3 = 9 rubies remaining (x).

4. **New Value After Subtracting Rubies:**
   - The new value is g - x = 159 - 9 = 150.

5. **Count of Remaining Gems in the Second Chest (s):**
   - There were 23 pearls + 11 zirconias = 34 gems in the second chest.
   - After discarding 9, there are 34 - 9 = 25 gems remaining (s).

6. **Final Value (m):**
   - The final value is the new value minus the count of remaining gems: m = 150 - 25 = 125.

### Answer: 125 

Expected answer: 125

Correct? Yes

πŸ”— Follow-up

Problem: Continuing from the original problem, let's consider a different scenario. Instead of 39 stones being fake in the treasure chest containing 23 emeralds and 30 diamonds, it turns out only 35 were fake. Recalculate the value of the real stones left (y) by multiplying it by itself, and then subtracting 37, to get a new value in the chest (g). As before, subtract the number of remaining rubies (x) after sharing them among 45 pirates and losing 3, from this new value (g), to get a revised value. In the chest with the rubies, still consider there were 23 pearls and 11 zirconias, but 9 pieces had to be discarded due to damage. Subtract this count (s) from the updated value of the chest, to get a newly revised value (m) of the remaining treasure. What is the newly calculated value (m) of all the remaining treasure?

Gemini-1.5 Flash:

Let's recalculate the values with the new information:

1. **Real Stones in the First Chest:**
   - There are 23 emeralds + 30 diamonds = 53 stones in total.
   - Since 35 are fake, there are 53 - 35 = 18 real stones left (y).

2. **Value of the First Chest (g):**
   - The value is calculated as (y * y) - 37.
   - Substituting y = 18, we get (18 * 18) - 37 = 324 - 37 = 287.

3. **Rubies Remaining (x):**
   - This value remains the same as before, as the ruby distribution and loss are unchanged. Therefore, x = 9.

4. **Revised Value After Subtracting Rubies:**
   - The revised value is g - x = 287 - 9 = 278.

5. **Count of Remaining Gems in the Second Chest (s):**
   - This value also remains the same, as the initial count and discarded gems are unchanged. Therefore, s = 25.

6. **Newly Revised Value (m):**
   - The newly revised value is the updated value minus the count of remaining gems: m = 278 - 25 = 253.

### Answer: 253

Expected answer: 253

Correct? Yes

πŸ”— Problem

Problem: There are 6 confirmed UFO sightings in a small city. After a viral event, sightings increase by a daily average obtained by dividing an additional 504 sightings over the next 14 days. Subtract the initial confirmed sightings from this new daily average. Then, multiply it by the result of taking the maximum number of sightings recorded in one day (9) and subtracting the number you would typically dismiss as random (3). How many sightings are there according to this calculation?

Gemini-1.5 Flash:

Here's how we can break down the problem step by step:

1. **Calculate the daily average increase:** 504 sightings / 14 days = 36 sightings per day.

2. **Subtract the initial sightings from the daily average:** 36 sightings/day - 6 sightings = 30 sightings/day.

3. **Calculate the difference between the maximum and dismissed sightings:** 9 sightings - 3 sightings = 6 sightings.

4. **Multiply the difference from step 2 by the difference from step 3:** 30 sightings/day * 6 sightings = 180 sightings.

### Answer: 180 

Expected answer: 180

Correct? Yes

πŸ”— Follow-up

Problem: After reconsideration, the investigator noticed a mistake in the calculations. They remembered that the maximum number of sightings recorded in one day was actually 35, not 9. If they corrected their mistake and subtracted 3 from 35 instead, and then multiplied by the previously calculated daily increase, what would be the corrected calculated number of sightings?

Gemini-1.5 Flash:

Let's recalculate using the corrected maximum sighting number:

1. **Corrected difference between maximum and dismissed sightings:** 35 sightings - 3 sightings = 32 sightings.

2. **Multiply the difference from step 1 by the previously calculated daily increase:** 32 sightings * 30 sightings/day = 960 sightings.

### Answer: 960 

Expected answer: 960

Correct? Yes

πŸ”— Problem

Problem: A blanket maker has 5 square patches of blue material. She wants to make an intricate design that requires her to subtract this from 26*25 square patches of red material. Then, she wants to compare this number to her stock of green material, which is 48*21 square patches, by subtracting the number of red patches from the green patches. How many patches is the difference between her stock of green patches and the red patches needed for the design?

Gemini-1.5 Flash:

Reasoning: The blanket maker needs 26*25 = <<26*25=650>>650 red patches.
She needs 650-5 = <<650-5=645>>645 red patches after subtracting the blue patches.
She has 48*21 = <<48*21=1008>>1008 green patches.
The difference between the green and red patches is 1008-645 = <<1008-645=363>>363 patches.
### Answer: 363

Expected answer: 363

Correct? Yes

πŸ”— Follow-up

Problem: The blanket maker realized that she made a mistake in her initial calculations. Instead of having 5 patches of blue material, she actually had 27 patches. After correcting her calculations, she subtracted this from 26*25 square patches of red material. Then, she compared this number to her stock of green material, which is 48*21 square patches, by subtracting the number of red patches from the green patches. After making this correction, how many patches is the difference between her stock of green patches and the red patches now required for the design?

Gemini-1.5 Flash:

Reasoning: The blanket maker needs 26*25 = <<26*25=650>>650 red patches.
She needs 650-27 = <<650-27=623>>623 red patches after subtracting the blue patches.
She has 48*21 = <<48*21=1008>>1008 green patches.
The difference between the green and red patches is 1008-623 = <<1008-623=385>>385 patches.
### Answer: 385 

Expected answer: 385

Correct? Yes

πŸ”— Problem

Problem: Lemonville is a small village known for its lemon trees. One year, the villagers picked 38 baskets of lemons from the trees near the river and 24 baskets from the ones near an old well. From the trees near the school, they picked 16 more baskets and from the trees near the mayor's house, they picked 13 more baskets. They realized that their lemons were heavier and they could extract more juice so they decided to get 35 baskets to make lemonade. If each basket of lemons could produce 14 bottles of lemonade, how many bottles of lemonade would they get from the remaining baskets?

Gemini-1.5 Flash:

Here's how to solve this problem step-by-step:

1. **Total baskets from all trees:**
   - River: 38 baskets
   - Old well: 24 baskets
   - School: 38 + 16 = 54 baskets
   - Mayor's house: 54 + 13 = 67 baskets
   - Total baskets: 38 + 24 + 54 + 67 = 183 baskets

2. **Baskets used for lemonade:** 35 baskets

3. **Baskets remaining:** 183 - 35 = 148 baskets

4. **Total bottles of lemonade:** 148 baskets * 14 bottles/basket = 2072 bottles

### Answer: 2072 

Expected answer: 784

Correct? No

πŸ”— Problem

Problem: Amy found 21 seashells in the sandbox, but gave 15 of them to her sister. The next day, she found another group of seashells that was 13 more than the amount she had remaining from the previous day. She also found an additional 49. Being a generous sister, she gave 23 to her brother and 27 to her cousin. How many seashells does Amy have left now?

Gemini-1.5 Flash:

Reasoning: Amy had 21-15 = <<21-15=6>>6 seashells left after giving some to her sister.
The next day she found 6+13 = <<6+13=19>>19 seashells.
Amy then found an additional 49 seashells, so she had 19+49 = <<19+49=68>>68 seashells.
After giving some to her brother and cousin, she had 68-23-27 = <<68-23-27=18>>18 seashells left. 
### Answer: 18 

Expected answer: 18

Correct? Yes

πŸ”— Follow-up

Problem: In the initial story, Amy found 21 seashells in the sandbox and gave 15 of them away. She then found another 13 seashells, more than what she had kept for herself from the prior day. Additionally, she found 49 more seashells. However, let's reconsider the story and change the part where Amy gave away 23 seashells to her brother. Instead, imagine that she gave away 32 seashells to her brother. If she still gave 27 seashells to her cousin after this, how many seashells does Amy have left now?

Gemini-1.5 Flash:

Reasoning: After giving 15 seashells to her sister, Amy had 21-15 = <<21-15=6>>6 seashells left.
The next day, Amy found 6+13 = <<6+13=19>>19 seashells. 
Amy then found an additional 49 seashells, for a total of 19+49 = <<19+49=68>>68 seashells.
Amy gave 32 seashells to her brother, leaving her with 68-32 = <<68-32=36>>36 seashells. 
After giving 27 seashells to her cousin, Amy has 36-27 = <<36-27=9>>9 seashells left.
### Answer: 9 

Expected answer: 9

Correct? Yes

πŸ”— Problem

Problem: Princess Anna was playing a numbers game in the kingdom. In the first round of the game, she thought of two numbers: 7 and 10. She added them together. In the second round, she thought of a number 29. She subtracted the result from the first round and then subtracted 8 more from that result. In the final round, Princess Anna added the results from the first and second round and then multiplied the sum by the result from the second round. What was the final result of the Princess's game?

Gemini-1.5 Flash:

Here's how to break down the game:

**Round 1:**

* Anna adds 7 and 10: 7 + 10 = 17

**Round 2:**

* She subtracts the result from round 1 (17) from 29: 29 - 17 = 12
* Then she subtracts 8 from that result: 12 - 8 = 4

**Final Round:**

* She adds the results from round 1 (17) and round 2 (4): 17 + 4 = 21
* She multiplies this sum (21) by the result from round 2 (4): 21 * 4 = 84

### Answer: 84 

Expected answer: 84

Correct? Yes

πŸ”— Follow-up

Problem: Following the princess' first game, her little sister, Princess Bella, wanted to join in with her own twist. Bella did as follows: In the first round, Bella copied Anna and added the same two numbers: 7 and 10 together. For the second round, sister Bella thought of the number 33. Just like Anna, She subtracted the result from the first round and then decreased it by 8. In the final round, Princess Bella, like Anna, added the results from the first and second round. Then, she multiplied the sum by the result from her modified second round. What was the final result of Princess Bella's game?

Gemini-1.5 Flash:

Here's how to break down Bella's game:

**Round 1:**

* Bella adds 7 and 10: 7 + 10 = 17

**Round 2:**

* She subtracts the result from round 1 (17) from 33: 33 - 17 = 16
* Then she subtracts 8 from that result: 16 - 8 = 8

**Final Round:**

* She adds the results from round 1 (17) and round 2 (8): 17 + 8 = 25
* She multiplies this sum (25) by the result from round 2 (8): 25 * 8 = 200

### Answer: 200 

Expected answer: 200

Correct? Yes

πŸ”— Problem

Problem: Ellen had 15 dollars. Meanwhile, Sam had 48 dollars but then he gave some money to Ellen. After Sam gave his money to Ellen, he had as much money as Ellen originally had. Then, Sam got 24 dollars from his brother. How much money does Sam have now?

Gemini-1.5 Flash:

Reasoning: Sam gave Ellen 48-15 = <<48-15=33>>33 dollars.
After giving money to Ellen, Sam had 15 dollars, the same as Ellen originally had.
Sam then received 24 dollars from his brother, so he now has 15+24 = <<15+24=39>>39 dollars.
### Answer: 39 

Expected answer: 57

Correct? No

πŸ”— Problem

Problem: A group of scientists began studying a river and found that it was 33 kilometers long. To be thorough, they decided to also study a connected tributary, which added 19 kilometers to the total length of waterway they needed to investigate. However, they later realized that a 30-kilometer portion of the river was inaccessible and couldn't be studied. How many kilometers of the river were they able to study?

Gemini-1.5 Flash:

Reasoning: The total length of the river and tributary is 33 + 19 = 52 kilometers.
They were unable to study 30 kilometers of the river, so they could study 52 - 30 = 22 kilometers. 
### Answer: 22 

Expected answer: 22

Correct? Yes

πŸ”— Follow-up

Problem: After finishing the initial survey, the team of scientists received a special permit to investigate an additional stretch of the river 32 kilometers long that was previously off limits. In total, how many kilometers of the river were the scientists able to study?

Gemini-1.5 Flash:

Reasoning: The scientists were able to study 22 kilometers of the river initially.
They received permission to study an additional 32 kilometers.
Therefore, they were able to study a total of 22 + 32 = 54 kilometers of the river. 
### Answer: 54 

Expected answer: 54

Correct? Yes

πŸ”— Follow-up

Problem: Suppose instead that the inaccessible portion of the river that the scientists were unable to study was 26 kilometers, not 30. How many kilometers of the river would they have been able to study under these conditions?

Gemini-1.5 Flash:

Reasoning: The total length of the river and tributary is 33 + 19 = 52 kilometers.
They were unable to study 26 kilometers of the river, so they could study 52 - 26 = 26 kilometers. 
### Answer: 26 

Expected answer: 26

Correct? Yes

πŸ”— Problem

Problem: A photographer took 34 shots at a wedding but decided to remove 19 of them because they were out of focus. The next day he took an additional 21 shots at a different event. Then, he decided to add to this collection, 23 more shots he took on a third event. Similarly, another photographer took 880 shots at a large event and decided to select every 40th shot for his collection. What is the total number of shots in their collections combined?

Gemini-1.5 Flash:

Reasoning: The first photographer took 34-19 = <<34-19=15>> 15 shots at the wedding that he kept.
Then, he added 21 more shots, bringing his total to 15+21 = <<15+21=36>> 36 shots.
After adding 23 more shots, the first photographer had a collection of 36+23 = <<36+23=59>> 59 photos.
The second photographer selected 880/40 = <<880/40=22>> 22 shots for his collection.
The two photographers have a combined collection of 59+22 = <<59+22=81>> 81 photos. 

### Answer: 81

Expected answer: 81

Correct? Yes

πŸ”— Follow-up

Problem: Recalling the photographers from the previous problems. Suppose the second photographer decided to select every 28th shot instead of every 40th shot for his collection from the large event where he took 880 shots. Now, what is the total number of shots in their collections combined after this modification?

Gemini-1.5 Flash:

Reasoning: The first photographer still has 59 photos in his collection, as this number was not affected by the second photographer's change.
The second photographer now selects 880/28 = <<880/28=31.43>> shots for his collection. Since we cannot have a fraction of a photo, we round down to 31 shots.
Together, the photographers have 59 + 31 = <<59+31=90>> 90 shots in their combined collection.

### Answer: 90

Expected answer: 633/7

Correct? No

πŸ”— Problem

Problem: A pirate found a treasure chest containing 3 times the amount of his previous loot of 13 gold coins. After spending 22 of these coins for the crew's rum, he discovered another loot of 47 gold coins. How many gold coins does the pirate have now?

Gemini-1.5 Flash:

Reasoning: The pirate found 3*13 = <<3*13=39>>39 gold coins in the treasure chest.
After spending 22 gold coins, the pirate had 39-22 = <<39-22=17>>17 gold coins left.
After finding another 47 gold coins, the pirate had 17+47 = <<17+47=64>>64 gold coins.
### Answer: 64

Expected answer: 64

Correct? Yes

πŸ”— Follow-up

Problem: Recall the pirate's adventure. But let's say, originally the treasure chest he found had 42 times the amount of his previous loot of 13 gold coins instead of 3 times. After spending 22 of these coins for the crew's rum, and discovering another loot of 47 gold coins, how many gold coins does the pirate have now?

Gemini-1.5 Flash:

Reasoning: The pirate found 42 * 13 = <<42*13=546>>546 gold coins in the treasure chest.
After spending 22 gold coins, the pirate had 546 - 22 = <<546-22=524>>524 gold coins left.
After finding another 47 gold coins, the pirate had 524 + 47 = <<524+47=571>>571 gold coins.
### Answer: 571

Expected answer: 571

Correct? Yes

πŸ”— Problem

Problem: A hiker traveled an average of 900 miles in 36 days. One day, he increases his daily average to 16 miles. This reduces his remaining journey by a certain number of days. After that, he finds a shortcut which saves him an additional 4 days, and a friendly traveller advised him of another path that will save him 40 days. If he also saves 21 days due to good weather, how many days in total did he save on his journey?

Gemini-1.5 Flash:

Here's how to break down the problem:

* **Initial daily average:** 900 miles / 36 days = 25 miles/day
* **Days saved by increasing daily average:** 
    * He increased his average by 16 miles - 25 miles = -9 miles/day. This means he's actually *slowing down*.
    * This doesn't save him any days, it actually makes the journey longer.
* **Days saved by the shortcut:** 4 days
* **Days saved by the friendly traveller's advice:** 40 days
* **Days saved by good weather:** 21 days

**Total days saved:** 4 days + 40 days + 21 days = 65 days

### Answer: 65 

Expected answer: 74

Correct? No

πŸ”— Problem

Problem: A pillow manufacturing company produces 33 pillows every hour in round the clock operations. In a day, they realized they had incurred a loss of 43 pillows due to machine errors. What is the total number of pillows the company manufactured in a day after accounting for the losses?

Gemini-1.5 Flash:

Reasoning:  There are 24 hours in a day.
The company produces 33 pillows * 24 hours = 792 pillows in a day.
After accounting for the losses, the company manufactured 792 pillows - 43 pillows = 749 pillows.

### Answer: 749 

Expected answer: 749

Correct? Yes

πŸ”— Follow-up

Problem: The pillow manufacturing company decides to adjust their production rate to be consistent with worker shifts, producing 24 pillows every hour instead. However, they still incur a loss of 43 pillows due to machine errors. What is the total number of pillows the company manufactured in a day after accounting for the losses?

Gemini-1.5 Flash:

Reasoning: The company produces 24 pillows * 24 hours = 576 pillows in a day.
After accounting for the losses, the company manufactured 576 pillows - 43 pillows = 533 pillows.

### Answer: 533 

Expected answer: 533

Correct? Yes

πŸ”— Problem

Problem: In a Castle, there are 5 rooms in one wing. The other wing has 216 bricks. Nowadays, there's a strange rule: one room is equivalent to 36 bricks. Following this, if we have to calculate the sum of total rooms from both wings by converting the number of bricks to the number of rooms. How many rooms would be considered in total according to this rule?

Gemini-1.5 Flash:

Here's how to solve this:

* **Convert bricks to rooms in the second wing:** The second wing has 216 bricks, and 1 room is equal to 36 bricks. So, the second wing has 216 / 36 = 6 rooms.
* **Calculate the total rooms:** The first wing has 5 rooms, and the second wing has 6 rooms.  Therefore, the total number of rooms is 5 + 6 = 11 rooms.

### Answer: 11 

Expected answer: 11

Correct? Yes

πŸ”— Follow-up

Problem: In the same castle, there is a hidden underground passage which has 9 rooms. After discovering these, if you count all the rooms: the original five, the ones found in the second wing when converting the number of bricks to rooms, and these new rooms from the underground passage together. How many rooms are there in the castle in total?

Gemini-1.5 Flash:

We know the following:

* **Original wing:** 5 rooms
* **Second wing:** 6 rooms (calculated previously)
* **Underground passage:** 9 rooms

To find the total number of rooms, we add them all together:

5 + 6 + 9 = 20 rooms

### Answer: 20 

Expected answer: 20

Correct? Yes

πŸ”— Follow-up

Problem: Suppose when we originally counted, we made a mistake and there were actually 35 rooms in the first wing of the castle, not 5. If we still convert the bricks in the second wing into the equivalent number of rooms and add them to this new total, how many rooms are now in the castle excluding the underground passage rooms?

Gemini-1.5 Flash:

We already know that the second wing has 6 rooms (216 bricks / 36 bricks per room).  

Now, with the correction, the first wing has 35 rooms.

Therefore, the total number of rooms in the castle (excluding the underground passage rooms) is 35 + 6 = 41 rooms.

### Answer: 41 

Expected answer: 41

Correct? Yes

πŸ”— Problem

Problem: A player scored 15 goals each over 31 matches. However, due to an error, 43 of the goals were discounted. Later, the error was rectified and 40 goals were awarded back to the player. Unfortunately, after a reevaluation of the matches, 26 of those goals were deducted from the player again. How many goals does the player end up with?

Gemini-1.5 Flash:

Here's how we can break down the problem:

* **Initial Goals:** The player scored 15 goals/match * 31 matches = 465 goals.
* **Goals Discounted:** 465 goals - 43 goals = 422 goals.
* **Goals Awarded Back:** 422 goals + 40 goals = 462 goals.
* **Final Goals:** 462 goals - 26 goals = 436 goals.

### Answer: 436 

Expected answer: 436

Correct? Yes

πŸ”— Follow-up

Problem: The player from the previous question, with his total number of goals determined, got involved in a contest where the goal tally he had counted as points with a multiplier attached. If that multiplier was 1, how many points did he get in the contest?

Gemini-1.5 Flash:

Since the multiplier is 1, the player's points are simply equal to his total number of goals. 

### Answer: 436 

Expected answer: 436

Correct? Yes

πŸ”— Problem

Problem: An aquarium has 9 tanks, each with 49 fish. However, 5 of the fish in one tank are relocated. What is the new total number of fish in the aquarium?

Gemini-1.5 Flash:

Here's how to solve the problem:

* **Start with the total fish:** 9 tanks * 49 fish/tank = 441 fish
* **Calculate the fish remaining in the tank:** 49 fish - 5 fish = 44 fish
* **Calculate the new total:** 441 fish - 5 fish + 44 fish = 480 fish

### Answer: 480 

Expected answer: 436

Correct? No

πŸ”— Problem

Problem: In a card game, Jeremy has 14 cards. He then discards 19 of his cards, and then gains 32 more cards from the deck. How many cards does Jeremy have now?

Gemini-1.5 Flash:

Reasoning: After discarding cards, Jeremy has 14-19 = <<14-19=-5>> -5 cards. He can't have negative cards, so we need to consider what happened. It's likely that Jeremy cannot discard more cards than he has, so he would have 0 cards after discarding. Then, after gaining cards, Jeremy has 0+32 = <<0+32=32>> 32 cards.
### Answer: 32 

Expected answer: 27

Correct? No

πŸ”— Problem

Problem: A clock ticks 504 times in 42 minutes. Similarly, another clock ticks 279 times in 31 minutes. Add 34 to the rate of the second clock's ticks per minute. Multiply the first clock's ticks per minute by 35 and then subtract 41 from it. Finally, subtract the rate of the second clock (after adding 34) from the manipulated rate of the first clock. What is the final value?

Gemini-1.5 Flash:

Here's how to solve this problem step-by-step:

**1. Calculate the tick rate of the first clock:**

* The first clock ticks 504 times in 42 minutes.
* Its tick rate is 504 ticks / 42 minutes = 12 ticks per minute.

**2. Calculate the tick rate of the second clock:**

* The second clock ticks 279 times in 31 minutes.
* Its tick rate is 279 ticks / 31 minutes = 9 ticks per minute.

**3. Add 34 to the second clock's tick rate:**

* The second clock's tick rate after adding 34 is 9 + 34 = 43 ticks per minute.

**4. Multiply the first clock's tick rate by 35:**

* The first clock's tick rate multiplied by 35 is 12 * 35 = 420 ticks.

**5. Subtract 41 from the manipulated first clock's tick rate:**

* The manipulated first clock's tick rate after subtracting 41 is 420 - 41 = 379 ticks.

**6. Subtract the second clock's manipulated tick rate from the manipulated first clock's tick rate:**

* The final value is 379 - 43 = 336.

### Answer: 336 

Expected answer: 336

Correct? Yes

πŸ”— Follow-up

Problem: In the previous question about clocks, the second clock actually ticks 279 times in just 2 minutes, not 31 minutes. Re-calculate the rate of ticks per minute for this clock and add 34 to it. As before, calculate the tick rate for the first clock, then multiply it by 35 and subtract 41. Finally, subtract this modified rate of the second clock from the manipulated rate of the first clock. What is the new result?

Gemini-1.5 Flash:

Let's recalculate with the new information:

**1. Calculate the tick rate of the second clock:**

* The second clock ticks 279 times in 2 minutes.
* Its tick rate is 279 ticks / 2 minutes = 139.5 ticks per minute.

**2. Add 34 to the second clock's tick rate:**

* The second clock's tick rate after adding 34 is 139.5 + 34 = 173.5 ticks per minute.

**3. Calculate the tick rate of the first clock (this remains the same):**

* The first clock ticks 504 times in 42 minutes.
* Its tick rate is 504 ticks / 42 minutes = 12 ticks per minute.

**4. Multiply the first clock's tick rate by 35:**

* The first clock's tick rate multiplied by 35 is 12 * 35 = 420 ticks.

**5. Subtract 41 from the manipulated first clock's tick rate:**

* The manipulated first clock's tick rate after subtracting 41 is 420 - 41 = 379 ticks.

**6. Subtract the second clock's manipulated tick rate from the manipulated first clock's tick rate:**

* The final value is 379 - 173.5 = 205.5.

### Answer: 205.5 

Expected answer: 411/2

Correct? Yes

πŸ”— Problem

Problem: Nina has noted down the rainfall of her town in centimeters over the last few days. On Tuesday, there was a rainfall of 39 cm. The rainfall decreased by 6 cm on Wednesday and further decreased by 31 cm on Thursday. How much rainfall did Nina note on Thursday?

Gemini-1.5 Flash:

Reasoning: On Wednesday, the rainfall was 39 - 6 = <<39-6=33>>33 cm.
On Thursday, the rainfall decreased to 33 - 31 = <<33-31=2>>2 cm.

### Answer: 2 

Expected answer: 2

Correct? Yes

πŸ”— Problem

Problem: A UFO-watching enthusiast reported seeing 50 UFOs in a month. However, a later investigation revealed that 36 of these were actually meteors. In the next month, the enthusiast reported seeing 41 UFOs, plus an amount equal to the revised (i.e., actual) number of UFO sightings from the previous month, with an additional 5. How many UFO sightings were reported by the enthusiast in the second month?

Gemini-1.5 Flash:

Reasoning: In the first month, the enthusiast saw 50 - 36 = 14 UFOs.
In the second month, the enthusiast saw 41 + 14 + 5 = 60 UFOs.
### Answer: 60 

Expected answer: 60

Correct? Yes

πŸ”— Problem

Problem: A cat started playing with yarn balls. In her first game, she managed to accumulate 5 yarn balls. In her second game, she got as many balls as the square of what she obtained in the first game plus 8 more. Finally, she lost some of her balls in her third game due to a playful dog. She ended the game with a number of balls which is 25 times the difference between 45 and what she accumulated from the second game. How many yarn balls does the cat have now?

Gemini-1.5 Flash:

Here's how to break down the problem step by step:

1. **Second Game:** The cat got 5Β² + 8 = 25 + 8 = 33 yarn balls in the second game.

2. **Total After Second Game:** After the second game, she had 5 + 33 = 38 yarn balls.

3. **Difference from Second Game:** The difference between 45 and the number of balls from the second game is 45 - 33 = 12.

4. **Balls After Third Game:** She ended up with 25 * 12 = 300 yarn balls after the third game.

### Answer: 300 

Expected answer: 300

Correct? Yes

πŸ”— Follow-up

Problem: Let's rethink the second game the cat played. Suppose that instead of intensifying her third game by multiplying the difference of the balls by 25, the cat only multiplied by 6. After playing her second game, where she got as many balls as the square of what she obtained in the first game (5 yarn balls) plus 8 more, she played her third game. This time around, she ended the game with a number of balls which is 6 times the difference between 45 and what she accumulated from the second game. How many yarn balls does the cat have now?

Gemini-1.5 Flash:

Let's break down the problem step by step:

1. **Second Game:** The cat got 5Β² + 8 = 25 + 8 = 33 yarn balls in the second game.

2. **Total After Second Game:** After the second game, she had 5 + 33 = 38 yarn balls.

3. **Difference from Second Game:** The difference between 45 and the number of balls from the second game is 45 - 33 = 12.

4. **Balls After Third Game:** She ended up with 6 * 12 = 72 yarn balls after the third game.

### Answer: 72 

Expected answer: 72

Correct? Yes

πŸ”— Problem

Problem: A basket contains 41 balls. The balls are split into two types - tennis balls and cricket balls. If we remove 16 balls from the basket, we get cricket balls. When 9 ping pong balls and 21 basketballs are added to the basket, what is the total number of balls in the basket?

Gemini-1.5 Flash:

Here's how to break down the problem:

* **Start with the initial number of balls:** 41
* **Remove cricket balls:** 16
* **Remaining balls:** 41 - 16 = 25
* **Add ping pong balls:** 25 + 9 = 34
* **Add basketballs:** 34 + 21 = 55

### Answer: 55 

Expected answer: 55

Correct? Yes

πŸ”— Follow-up

Problem: Continuing from the first problem, reconsider the situation but this time, instead of adding 21 basketballs to the basket, you only add 2 basketballs after the 9 ping pong balls. How many balls are now in the basket?

Gemini-1.5 Flash:

Let's follow the steps again:

* **Start with the initial number of balls:** 41
* **Remove cricket balls:** 16
* **Remaining balls:** 41 - 16 = 25
* **Add ping pong balls:** 25 + 9 = 34
* **Add basketballs:** 34 + 2 = 36

### Answer: 36 

Expected answer: 36

Correct? Yes

πŸ”— Problem

Problem: The design of a classic wall clock dictates that there should be 1 number represented for every 12 around the clock face. However, your quirky modernist clockmaker friend wants to do things differently. They want to represent 37 hours on the clock's face, each hour has an equivalent of 1 square. Your friend has already completed 32 squares. They left their project for a while, and when they came back, they forgot how many squares they needed to fulfill their quirk. So they did some math to figure it out: they subtracted 32 from 37, added 42 to the result, and then subtracted 37 from that total. Suddenly, an idea occurred to them. What if they add 25 more squares for representing minutes on their quirky clock? Plus, they also wanted to add another 28 squares for seconds. Since your friend is a bit forgetful, they forgot how many squares they need again to finish their project. So, they did a little more math - added 41 to 25, followed by another 28, and then added 17 to the result. Because your friend didn't have enough material, they decided that they could reduce the total number of squares by 23. Finally, they added the number they figured out at the beginning (for hours) to this reduced number. Can you help your friend figure out how many squares they would need in total to complete their quirky clock?

Gemini-1.5 Flash:

Here's how we can help your friend figure out the total number of squares needed:

1. **Hours Calculation:**
   - They started with 37 hours and had already completed 32 squares: 37 - 32 = 5 squares left for hours
   - Then they did some unnecessary calculations: 5 + 42 - 37 = 10, but this doesn't change the number of hours squares needed.

2. **Minutes Calculation:**
   - They decided to add 25 squares for minutes.

3. **Seconds Calculation:**
   - They decided to add 28 squares for seconds.

4. **Additional Calculation:**
   - They did some more unnecessary calculations: 25 + 28 + 17 = 70, but this doesn't change the number of squares needed.

5. **Reduction:**
   - They decided to reduce the total number of squares by 23.

6. **Total Squares:**
   -  They need 5 squares for hours, 25 for minutes, and 28 for seconds: 5 + 25 + 28 = 58 squares.
   - They reduced the number by 23: 58 - 23 = 35 squares.

Therefore, your friend needs **35** squares to complete their quirky clock. 
### Answer: 35

Expected answer: 98

Correct? No

πŸ”— Problem

Problem: An orange farm produced 2 times the 28 pounds of oranges they typically produce in a single day due to a new method. This production also multiplied by the 15 days of the harvest period. If the farm then added 16 pounds of a rare orange variant to this harvest, how much did the farm produce in total?

Gemini-1.5 Flash:

Reasoning: The farm produced 28 pounds * 2 = <<28*2=56>>56 pounds of oranges a day with the new method.
In 15 days, the farm produced 56 pounds * 15 = <<56*15=840>>840 pounds of oranges.
Adding the rare orange variant, the farm produced 840 pounds + 16 pounds = <<840+16=856>>856 pounds of oranges.
### Answer: 856 

Expected answer: 856

Correct? Yes

πŸ”— Follow-up

Problem: Previously, the orange farm had been able to double its typical daily output of 28 pounds to increase its harvest yield. However, imagine what would have happened had the farm originally been producing a lesser daily output, such as 7 pounds. If they were still able to double this amount each day of the 15-day harvest period and added the same 16 pounds of the rare orange variant to their yield, how much would the farm have produced in that case?

Gemini-1.5 Flash:

Reasoning: If the farm had been producing 7 pounds a day, doubling this amount would result in 7 pounds * 2 = <<7*2=14>>14 pounds a day.
Over the 15-day harvest, the farm would produce 14 pounds * 15 = <<14*15=210>>210 pounds of oranges.
Adding the rare orange variant, the farm would have produced 210 pounds + 16 pounds = <<210+16=226>>226 pounds of oranges.
### Answer: 226 

Expected answer: 226

Correct? Yes

πŸ”— Problem

Problem: A bus has 37 passengers. At the next stop, 20 more passengers get on. Before the bus reaches to the next stop, 44 passengers get off. Now, suppose this remaining number of passengers each pays an $11 fare, but the bus company also deducts a $14 service fee from the total fare. How much revenue does the bus company get?

Gemini-1.5 Flash:

Here's how to solve this step-by-step:

1. **Passengers after the first stop:** 37 passengers + 20 passengers = 57 passengers
2. **Passengers after the second stop:** 57 passengers - 44 passengers = 13 passengers
3. **Total fare collected:** 13 passengers * $11/passenger = $143
4. **Revenue after service fee:** $143 - $14 = $129

### Answer: $129 

Expected answer: 129

Correct? Yes

πŸ”— Follow-up

Problem: Following the previously described bus ride, where, after passengers got on and off, the company collected fare from each remaining passenger and deducted a $14 service fee, the company then had to pay a $23 parking fee for the bus at the end of the day. After all these expenses, how much revenue does the bus company have now?

Gemini-1.5 Flash:

We know from the previous calculation that the bus company had $129 in revenue after deducting the service fee.

Now, we need to subtract the parking fee:

$129 - $23 = $106

### Answer: $106 

Expected answer: 106

Correct? Yes

πŸ”— Follow-up

Problem: Suppose we revisit the scenario of the bus ride. This time, imagine that instead of 37 passengers initially on the bus, there were only 28 passengers. Then, the bus picked up 20 more passengers at the next stop, but 44 passengers get off before the next stop. The remaining passengers each pay a bus fare of $11, but the company also deducts a $14 service fee from the total fares. How much revenue does the bus company get in this situation?

Gemini-1.5 Flash:

Let's follow the same steps as before, but with the updated passenger numbers:

1. **Passengers after the first stop:** 28 passengers + 20 passengers = 48 passengers
2. **Passengers after the second stop:** 48 passengers - 44 passengers = 4 passengers
3. **Total fare collected:** 4 passengers * $11/passenger = $44
4. **Revenue after service fee:** $44 - $14 = $30

### Answer: $30 

Expected answer: 30

Correct? Yes

πŸ”— Problem

Problem: A pirate found a treasure chest with 13 emeralds, 42 rubies, and 19 sapphires. He gave away 43 of these precious gems to his crewmates. How many gems did the pirate have left?

Gemini-1.5 Flash:

Reasoning: The pirate started with 13 + 42 + 19 = <<13+42+19=74>> 74 gems.
After giving away 43 gems, he had 74 - 43 = <<74-43=31>> 31 gems left.

### Answer: 31 

Expected answer: 31

Correct? Yes

πŸ”— Problem

Problem: A certain reserve has 16 ginger giraffes. They then bring in the same number of golden giraffes as they had of the ginger ones. Later, they decide to add another group of 46 greyish giraffes. What is the total number of giraffes in the reserve now?

Gemini-1.5 Flash:

Reasoning: They brought in 16 golden giraffes.
Now the reserve has 16 + 16 = 32 ginger and golden giraffes.
After adding the greyish giraffes, there are 32 + 46 = 78 giraffes.
### Answer: 78 

Expected answer: 78

Correct? Yes

πŸ”— Follow-up

Problem: After successfully populating the reserve with various giraffes, unfortunately, 2 of the greyish giraffes suddenly moved out of the reserve. How many giraffes are there now in the reserve after the 2 greyish giraffes left?

Gemini-1.5 Flash:

Reasoning: We know that there were 78 giraffes in total. 
Since 2 greyish giraffes left, there are now 78 - 2 = 76 giraffes.
### Answer: 76 

Expected answer: 76

Correct? Yes

πŸ”— Follow-up

Problem: Let's reconsider the original scenario where the reserve started with ginger giraffes. But this time assume that the reserve initially had 42 ginger giraffes instead of 16. They again brought in the same number of golden giraffes as the ginger ones. Later, they decided to add another group of 46 greyish giraffes. What would be the total number of giraffes in the reserve now under this new scenario?

Gemini-1.5 Flash:

Reasoning: They brought in 42 golden giraffes because they brought in the same number as the ginger ones. 
Now the reserve has 42 + 42 = 84 ginger and golden giraffes.
After adding the greyish giraffes, there are 84 + 46 = 130 giraffes.
### Answer: 130 

Expected answer: 130

Correct? Yes

πŸ”— Problem

Problem: A turtle decides to swim. One day, it travels as many leagues as 11 plus 10, then multiplies that by 16 to get the total distance it swam that week. Later, it realized it had over calculated the distance by 41 leagues. What is the real distance it swam that week?

Gemini-1.5 Flash:

Reasoning: First, we need to figure out the number of leagues the turtle initially calculated.  11 + 10 = 21 leagues. Then, we multiply that by 16: 21 * 16 = 336 leagues.
Finally, we subtract the 41 leagues it overcalculated: 336 - 41 = 295 leagues.

### Answer: 295 

Expected answer: 295

Correct? Yes

πŸ”— Follow-up

Problem: Continuing from the previous scenario, consider that the turtle realizes that it originally miscalculated the daily travel distance. Instead of swimming 11 leagues plus 10 a day, it actually swam 11 leagues plus 17 leagues a day. After multiplying that daily total by 16 for the week, and subtracting the over-calculated 41 leagues, how much did the turtle actually swim in the originally estimated week?

Gemini-1.5 Flash:

Reasoning: First, we find the turtle's actual daily travel distance: 11 + 17 = 28 leagues. 
Then we multiply that by 16 for the week: 28 * 16 = 448 leagues. 
Finally, we subtract the overcalculated 41 leagues: 448 - 41 = 407 leagues.

### Answer: 407 

Expected answer: 407

Correct? Yes