Problem: If we had a smaller beach ball that only required 1310 cubic centimeters of air to fully inflate, and we continue to fill it up at a rate of 41 cubic centimeters per second, how many seconds will it then take to inflate this smaller beach ball?

Gemini-1.5 Flash:

Reasoning: To find the time it takes to inflate the smaller ball, we need to divide the total volume of air needed by the inflation rate. This means we have to calculate 1310 / 41.

### Answer: 32 seconds. 

Expected answer: 1310/41

Correct? No

Problem: In the previous problem, the juice company produced 73528 liters of juice filled into 707 containers. Now consider instead that the juice company produced a new batch of fresh juice, a total of 2858 liters. If the new batch was also filled the same way into 707 containers, how many liters of juice are now in each container?

Gemini-1.5 Flash:

Reasoning: To find the amount of juice in each container for the new batch, we divide the total amount of juice in the new batch by the number of containers.

So, each container has 2858 / 707 = 4 liters of juice.

### Answer: 4 

Expected answer: 2858/707

Correct? No

Problem: If the pants factory had produced a total of 4003 pants instead of 87780, and still equally distributed them to the 110 wholesale clothing stores, how many pants would each store have received now?

Gemini-1.5 Flash:

Reasoning: To find out how many pants each store would receive, we need to divide the total number of pants by the number of stores: 4003 pants / 110 stores = 36.39 pants/store. Since we can't have a fraction of a pant, each store would receive 36 pants. 

### Answer: 36 

Expected answer: 4003/110

Correct? No

Problem: Farmer Bob reconsiders and decides to increase the size of each bundle. If he now distributes his 71820 carrots into bundles of 2486 each, how many bundles will he have?

Gemini-1.5 Flash:

Reasoning: To find out how many bundles Farmer Bob can make with the new bundle size, we need to divide the total number of carrots by the new number of carrots per bundle.
So, Farmer Bob will have 71820 / 2486 = <<71820/2486=28.90...>>  bundles of carrots. Since we can't have a fraction of a bundle, we round down to the nearest whole number.
### Answer: 28 

Expected answer: 35910/1243

Correct? No

Problem: After maintaining a consistent usage rate, the same slide has been used 9018 times over 54 consecutive days. Under this rate, how many times per day has the slide been used?

Gemini-1.5 Flash:

Reasoning: To find the usage rate per day, we divide the total usage by the number of days: 9018 times / 54 days = 167 times/day.

### Answer: 167 

Expected answer: 167

Correct? Yes

Problem: What if the snow was spread out not over 225 days, but over a period of 1814 days? How many inches of snow would the ski resort receive each day in this case?

Gemini-1.5 Flash:

Reasoning: To find the daily snowfall, we need to divide the total snowfall by the number of days. 
We have 31950 inches of snow / 1814 days = <<31950/1814=17.61>>17.61 inches of snow per day. 

### Answer: 17.61 

Expected answer: 15975/907

Correct? No

Problem: The jewelry manufacturer now has 5240 grams of gold instead of 63802 grams. If they still want to make each ring weigh exactly the same and produce 38 rings, how many grams of gold will be in each ring now?

Gemini-1.5 Flash:

Reasoning: To find the weight of each ring, we divide the total weight of gold by the number of rings.
This means each ring will weigh 5240 / 38 = 138 grams.
### Answer: 138 

Expected answer: 2620/19

Correct? No

Problem: Now consider that instead of 617 cages, the 10,489 animals are evenly distributed in 5130 cages. How does the average number of animals per cage change now?

Gemini-1.5 Flash:

Let's calculate the new average:

Average animals per cage = Total animals / Number of cages

Average animals per cage = 10489 / 5130

Average animals per cage ≈ 2.04

### Answer: 2.04 

Expected answer: 10489/5130

Correct? No

Problem: The farmer had initially thought he had 21652 grams of carrots. However, upon recounting, he realizes he actually has 5652 grams of carrots. If he still wants to distribute the carrots evenly into 5413 bags, how many grams of carrots will now be in each bag?

Gemini-1.5 Flash:

With the corrected amount of carrots, we need to divide the new total weight by the number of bags:

5652 grams / 5413 bags = 1.04 grams/bag (approximately)

### Answer: 1.04 

Expected answer: 5652/5413

Correct? No

Problem: In the previous space mission scenario, if instead, the spaceship had to divide its total travel distance of 38745 miles into 3113 equal stages, how many miles would it now have to travel in each stage?

Gemini-1.5 Flash:

Reasoning: To find out how many miles the spaceship travels in each stage, we need to divide the total distance by the number of stages. So, we need to calculate 38745 / 3113.

38745 / 3113 = <<38745/3113=12.48>>12.48 (approximately)

### Answer: 12.48 

Expected answer: 38745/3113

Correct? No

Problem: If the factory instead needed to distribute 84,564 liters of water evenly into 1,779 bottles, how many liters would each bottle contain now?

Gemini-1.5 Flash:

Reasoning: We need to divide the total amount of water (84,564 liters) by the number of bottles (1,779) to find out how many liters each bottle would contain. 

### Answer: 47.5 liters 

Expected answer: 28188/593

Correct? No

Problem: If instead of 2188 hours, the fireplace was working continuously for 3809 hours with the same total energy consumption of 56888 BTU, how many BTU of energy would the fireplace use per hour then?

Gemini-1.5 Flash:

Reasoning:  We need to divide the total energy used by the new number of hours.

So, the fireplace would use 56888 BTU / 3809 hours = 14.94 BTU/hour (approximately).

### Answer: 14.94 

Expected answer: 4376/293

Correct? No

Problem: In the same town, in another winter period, the total snowfall recorded was 36900 inches as well but this time across 7138 days. If the snow fell at a constant rate every day, how many inches of snow did the town receive each day during this period?

Gemini-1.5 Flash:

Reasoning: To find the daily snowfall, we divide the total snowfall by the number of days. 
So, the town received 36900 inches / 7138 days = <<36900/7138=5.18 (rounded to two decimal places)>> 5.18 inches of snow each day.

### Answer: 5.18 

Expected answer: 18450/3569

Correct? No

Problem: Suppose the wildlife reserve instead held 8787 giraffes that were spread out evenly across the 71292 square kilometers. In this case, how many square kilometers would each giraffe get?

Gemini-1.5 Flash:

Reasoning: To find the space per giraffe, we divide the total area by the number of giraffes: 71292 square kilometers / 8787 giraffes = 8.1 square kilometers per giraffe.

### Answer: 8.1 

Expected answer: 23764/2929

Correct? No

Problem: The mermaid realized that she had miscalculated and there are actually only 4198 mermaid friends, not 631. If she divides the 32812 pearls evenly among her 4198 friends now, how many pearls will each friend receive?

Gemini-1.5 Flash:

Reasoning:  Now that we know there are 4198 mermaid friends, we need to divide the total number of pearls (32812) by the number of friends.

32812 ÷ 4198 = 7.815 (approximately)

Since we can't have a fraction of a pearl, each friend would receive 7 pearls. 

### Answer: 7 

Expected answer: 16406/2099

Correct? No

Problem: Considering the previous situation, what if the farm actually produced the same number of apples over a much longer period of 152 weeks rather than 19 weeks? How many apples does the farm now produce weekly?

Gemini-1.5 Flash:

Reasoning:  Since the farm produces the same number of apples each week, the total number of apples produced over the entire growing season doesn't change. We simply need to divide the total number of apples by the new number of weeks. 

So, the farm now produces 36,784 / 152 = <<36784/152=242>> 242 apples weekly. 

### Answer: 242 

Expected answer: 242

Correct? Yes

Problem: Suppose the train now travels a total of 6280 miles over the same period of 695 days. If the train still travels the same distance each day, how many miles will it cover in a day now?

Gemini-1.5 Flash:

To find the distance the train covers in a day, we need to divide the total distance by the number of days. 

So, the train covers 6280 miles / 695 days =  9.03 miles per day (approximately).

### Answer: 9.03 

Expected answer: 1256/139

Correct? No

Problem: What if the same doll factory initially planned to produce the same total number of 41772 dolls, but now over a longer period of 4664 days? If so, how many dolls would have been produced daily then?

Gemini-1.5 Flash:

Reasoning: If the factory planned to produce the same total number of dolls over a longer period, the daily production rate would be lower.  We find this by dividing the total number of dolls by the new number of days. 

The factory would have produced 41772 / 4664 = <<41772/4664=9>>9 dolls per day.

### Answer: 9 

Expected answer: 10443/1166

Correct? No

Problem: The drummer realized that his initial goal was too lofty, and decided to reduce his goal to hitting his drum 7454 times instead. If he still plans to do this over the course of 7 days, how many times will he need to hit the drum each day to meet his new goal?

Gemini-1.5 Flash:

Reasoning: To find out how many times he needs to hit the drum each day, we need to divide his new total goal by the number of days: 7454 / 7 = 1065

### Answer: 1065 

Expected answer: 7454/7

Correct? No

Problem: Following the change, suppose now that the dolphin swam a total of 6186 meters within the same 128 hours. How many meters is the dolphin now swimming in an hour?

Gemini-1.5 Flash:

To find out the dolphin's new speed, we divide the total distance it swam (6186 meters) by the total time (128 hours).

6186 meters / 128 hours = 48.3 meters/hour.

### Answer: 48.3 

Expected answer: 3093/64

Correct? No

Problem: Suppose the compass salesman later realizes he made a mistake and that he actually has to distribute the 33046 compasses equally among 6456 stores, not 1066. How many compasses will each store receive now, if they are divided equally?

Gemini-1.5 Flash:

To find out how many compasses each store will receive now, we need to divide the total number of compasses by the new number of stores:

33046 compasses / 6456 stores = 5.11 compasses per store

Since we can't have a fraction of a compass, each store will receive 5 compasses.

### Answer: 5 

Expected answer: 16523/3228

Correct? No

Problem: Suppose in the same large farm, they only managed to produce a total of 9653 carrots from the same 58 plots the next year. If these plots yielded the same number of carrots, how many carrots did each plot yield this time?

Gemini-1.5 Flash:

To find out how many carrots each plot yielded this year, we need to divide the total number of carrots by the number of plots.

So, each plot yielded 9653 carrots / 58 plots = 166.43 carrots per plot (approximately).

Since we can't have fractions of carrots, we round down to the nearest whole number.

### Answer: 166 

Expected answer: 9653/58

Correct? No

Problem: If the scooter's total distance on a full charge was instead 7727 meters, keeping the battery life at 18 hours, how many meters would the scooter travel per hour now?

Gemini-1.5 Flash:

Reasoning:  We divide the new total distance by the battery life to find the distance traveled per hour. 
Therefore, the scooter travels 7727 meters / 18 hours = <<7727/18=429.28>>429.28 meters per hour.

### Answer: 429.28 

Expected answer: 7727/18

Correct? No

Problem: If instead, the star emitted a total of 94548 units of light energy over a shorter period of 3349 hours, still at a constant rate, how much light energy would it emit every hour now?

Gemini-1.5 Flash:

Reasoning:  We divide the total light energy by the new number of hours to find the new rate: 94548 units / 3349 hours = 28.24 units of light energy per hour (approximately).

### Answer: 28.24 

Expected answer: 94548/3349

Correct? No

Problem: Given the same forest as before with 80752 trees, what if it was divided into 1778 sections instead of 412? How many trees would there be in each section now?

Gemini-1.5 Flash:

To find the number of trees in each section, we need to divide the total number of trees by the number of sections: 80752 trees / 1778 sections = 45.34 trees/section.

Since we can't have a fraction of a tree, we round down to the nearest whole number.

### Answer: 45 

Expected answer: 5768/127

Correct? No

Problem: If instead of 44280 cucumbers, the farm only harvested 4076 cucumbers over the same 216 days, how many cucumbers were harvested each day given this new quantity?

Gemini-1.5 Flash:

Reasoning: We can find the number of cucumbers harvested each day by dividing the total number of cucumbers by the number of days.  

So, 4076 cucumbers / 216 days = 18.8 cucumbers/day. Since you can't harvest a fraction of a cucumber, we round down to the nearest whole number.

### Answer: 18 

Expected answer: 1019/54

Correct? No

Problem: Considering the same scenario where the cookie factory is producing cookies, imagine now they increased their packaging capabilities and packaged the same 77545 cookies into 1834 packages instead of 1193. How many cookies are there in each package now?

Gemini-1.5 Flash:

To find the number of cookies in each package with the increased packaging capacity, we need to divide the total number of cookies by the new number of packages:

77545 cookies / 1834 packages = 42.33 cookies/package (approximately)

Since we cannot have a fraction of a cookie, we round down to the nearest whole number.

### Answer: 42 

Expected answer: 77545/1834

Correct? No

Problem: If instead, over a different period, the star emitted 51750 units of light energy every 8670 seconds, how much light energy would it be emitting per second?

Gemini-1.5 Flash:

Reasoning: To find out how much light energy the star emits every second, we need to divide the total light energy emitted by the number of seconds.

Therefore, the star emits 51750 units / 8670 seconds = 5.97 units of light energy every second (rounded to two decimal places).

### Answer: 5.97 

Expected answer: 1725/289

Correct? No

Problem: In the previous scenario, suppose that the candy factory had instead produced 25144 candies evenly over 4290 days. How many candies would they have made each day in this case?

Gemini-1.5 Flash:

Reasoning:  To find out how many candies the factory made each day, we divide the total number of candies by the number of days. In this case, we divide 25144 by 4290.

25144 / 4290 = 5.86 (approximately)

Since we can't have fractions of candies, we round down to the nearest whole number.

### Answer: 5 

Expected answer: 12572/2145

Correct? No

Problem: If instead the party needed 7638 slices of bread for sandwiches, still considering that each loaf of bread contains 10 slices, how many loaves of bread would then be needed for the party?

Gemini-1.5 Flash:

Reasoning: To find out how many loaves are needed, we divide the total number of slices by the number of slices per loaf. 

This can be expressed as 7638 slices / 10 slices/loaf = 763.8 loaves.

Since we cannot have a fraction of a loaf, we round up to the nearest whole number.

### Answer: 764 

Expected answer: 3819/5

Correct? No

Problem: The same forest ranger now considers a different area of the forest. This time, over a period of 119 days, he noticed that 6216 new trees had sprouted. If the same number of new trees sprouted each day, how many new trees sprouted each day in this different area of the forest?

Gemini-1.5 Flash:

Reasoning: To find out how many trees sprout each day, we need to divide the total number of trees by the number of days. So, we have 6216 trees / 119 days = <<6216/119=52>>52 trees per day. 

### Answer: 52 

Expected answer: 888/17

Correct? No

Problem: Following the previous question, now consider that the same dog food factory distributed a different brand of dog food, this time totaling 5,981 cans, uniformly over the same 52 weeks. How many cans of this different brand of dog food did they distribute per week?

Gemini-1.5 Flash:

Reasoning: To find the number of cans distributed per week, we divide the total number of cans by the number of weeks.

5,981 cans / 52 weeks = 115.02 cans/week (approximately)

Since you can't distribute a fraction of a can, we round down to the nearest whole number.

### Answer: 115 

Expected answer: 5981/52

Correct? No

Problem: Following up on the previous scenario, the farmer discovered that he actually harvested a total of 7664 potatoes, not 45764. With the same number of plants (2692), what would be the new average of potatoes each plant produces?

Gemini-1.5 Flash:

Reasoning:  We need to recalculate the average by dividing the new total number of potatoes by the number of plants.

The new average is 7664 / 2692 = 2.85 (approximately).

### Answer: 2.85 

Expected answer: 1916/673

Correct? No

Problem: In the same marshmallow factory, another batch of marshmallows was made over a longer production period. This time, 85560 marshmallows were produced in 7544 hours. If the factory produces the same amount each hour during this period, how many marshmallalls were made each hour now?

Gemini-1.5 Flash:

Reasoning: To find out how many marshmallows are made each hour, we need to divide the total number of marshmallows by the number of hours. 
Therefore, the factory produces 85560/7544 = <<85560/7544=11.34>> marshmallows each hour. 
### Answer: 11.34 

Expected answer: 465/41

Correct? No

Problem: Instead of subdividing the total area of 49,928 square meters into plots of 6,241 square meters each, the farmer decides to subdivide it into smaller plots, each measuring 23 square meters. How many plots are there on the farm now?

Gemini-1.5 Flash:

To find the number of smaller plots, we need to divide the total area by the area of each smaller plot. 

Therefore, there are 49,928 square meters / 23 square meters/plot = 2,170.78 plots. Since you can't have a fraction of a plot, we round down to the nearest whole number.

### Answer: 2,170 

Expected answer: 49928/23

Correct? No

Problem: The baker realized that he actually used a total of 62118 grams of flour over the course of 2755 days, not 2142 days as previously thought. How does the daily use of flour for cookies change with this correction?

Gemini-1.5 Flash:

Reasoning: We can use the same formula as before: flour used per day = total flour / number of days. 
 
  With the corrected information, we have: 
 flour used per day = 62118 / 2755
 
 Therefore, the baker actually used 62118 / 2755 = <<62118/2755=22.55>>22.55 grams of flour each day. 
 
 Since the baker used more flour over a longer period of time, the daily flour usage is lower than previously calculated.

### Answer: 22.55 

Expected answer: 2142/95

Correct? No

Problem: If the shoemaker only had 9498 pairs of shoes but the same amount of shoelace (91100 centimeters), how many centimeters of shoelace would each pair get then?

Gemini-1.5 Flash:

Reasoning: If the shoemaker had 9498 pairs of shoes, each pair would get 91100/9498 = <<91100/9498=9.6>>9.6 centimeters of shoelace. 
### Answer: 9.6 

Expected answer: 45550/4749

Correct? No

Problem: The farmer has now harvested a bigger lot of 7798 bushels of apples and once again distributes them equally into 5 bins. Now, how many bushels of apples does each bin contain?

Gemini-1.5 Flash:

Reasoning:  To find out how many bushels are in each bin, we need to divide the total number of bushels by the number of bins.

7798 bushels / 5 bins = 1559.6 bushels per bin.  Since we can't have a fraction of a bushel, we round down to the nearest whole bushel.

### Answer: 1559 

Expected answer: 7798/5

Correct? No

Problem: What if instead, the total confetti pieces at the party were spread across 9944 square feet of area instead of 5025? How many confetti pieces would be there per square foot in that case?

Gemini-1.5 Flash:

Reasoning:  We can use the same equation as before: confetti pieces per square foot = total confetti pieces / total area.
In this case, the total area is 9944 square feet. 
Plugging in the values, we get: confetti pieces per square foot = 65325 / 9944.

Therefore, there would be 65325/9944 = 6.57 (approximately) confetti pieces per square foot.

### Answer: 6.57 (approximately) 

Expected answer: 65325/9944

Correct? No

Problem: Suppose the crayon factory now produced 4521 crayons instead of 26691, and these were still evenly distributed into 123 boxes. How many crayons would there be in each box under this new scenario?

Gemini-1.5 Flash:

Reasoning: Similar to the previous problem, we divide the total number of crayons by the number of boxes to find the number of crayons per box. 
So, 4521 crayons / 123 boxes = <<4521/123 = 36.75>>36.75 crayons per box. Since we can't have a fraction of a crayon, we would round down to 36 crayons per box.

### Answer: 36 

Expected answer: 1507/41

Correct? No

Problem: Following the previous scenario of the firefighter unit, suppose the total number of fires they actually extinguished over the period was 45843, but the time frame was 4913 weeks instead of 413 weeks. If they extinguished the same number of fires each week, how many fires did they extinguish per week now?

Gemini-1.5 Flash:

Reasoning: We need to divide the total number of fires extinguished by the number of weeks to find the number of fires extinguished per week. 
Therefore, the firefighter unit extinguished 45843 / 4913 = <<45843/4913=9.33>> 9.33 fires per week (approximately).

### Answer: 9.33 

Expected answer: 45843/4913

Correct? No

Problem: After re-evaluating the park layout, the park authority has decided to divide the 57546 square meter park into 131 identical sections instead of 9591. What is the area of each section in square meters now?

Gemini-1.5 Flash:

Reasoning: To find the area of each section, we divide the total area of the park by the number of sections: 57546 square meters / 131 sections = 439 square meters per section. 
### Answer: 439 

Expected answer: 57546/131

Correct? No

Problem: Suppose the toothpaste company changes its manufacturing process and is now able to produce only 9206 tubes of toothpaste with the same 4938 boxes of raw materials. If each box of raw materials still produces the same number of toothpaste tubes, how many toothpaste tubes are now generated from one box of raw materials?

Gemini-1.5 Flash:

Reasoning: With the new process, the company produces 9206 tubes of toothpaste using 4938 boxes of raw materials. To find out how many tubes are generated from one box, we need to divide the total number of tubes by the number of boxes: 9206 / 4938.

### Answer: 1.86 

Expected answer: 4603/2469

Correct? No

Problem: Imagine now that over a period of 84 days, 8576 children use the park's Jungle gym instead of 40740 children. If the Jungle gym is used equally by kids each day, how many children are now using the Jungle gym per day?

Gemini-1.5 Flash:

Reasoning: To find out how many children use the Jungle gym each day, we divide the total number of children by the number of days.
8576 / 84 = <<8576/84=102>> 102
### Answer: 102 

Expected answer: 2144/21

Correct? No

Problem: In the previous snowman competition, suppose that the organizers used only 5895 cc (cubic centimeters) of snow to make the same 38 identical snowmen. How many cubic centimeters of snow would be used for each snowman in this scenario?

Gemini-1.5 Flash:

Reasoning: To find out how much snow is used for each snowman, we need to divide the total amount of snow by the number of snowmen.

We have 5895 cc of snow and 38 snowmen. So, each snowman uses 5895 / 38 = 155 cc of snow.

### Answer: 155 

Expected answer: 5895/38

Correct? No

Problem: If the large window instead spanned a smaller area of 7562 square inches, and it is still being divided into 1147 equally sized smaller squares, now what would be the area in square inches of each of these smaller squares?

Gemini-1.5 Flash:

Reasoning: To find the area of each smaller square, we need to divide the total area of the large window by the number of smaller squares.  

So, the area of each smaller square is 7562 square inches / 1147 = <<7562/1147=6.6>> 6.6 square inches. 

### Answer: 6.6 

Expected answer: 7562/1147

Correct? No

Problem: Now, the farmer decided to distribute the same total number of 49,920 oranges but now only among 9,289 of his best-performing trees. How many oranges does each of these selected trees produce?

Gemini-1.5 Flash:

The farmer has 49,920 oranges and wants to distribute them evenly among 9,289 trees. To find out how many oranges each tree gets, we need to divide the total number of oranges by the number of trees. 

So, we have 49,920 oranges / 9,289 trees = 5.38 oranges per tree (approximately).

Since we can't have a fraction of an orange, we need to round this number. We can either round down to 5 oranges per tree or round up to 6 oranges per tree.

### Answer:  5 or 6 

Expected answer: 49920/9289

Correct? No

Problem: In the same consumption study, it was later revealed that the actual number of children who had a sandwich for lunch is 34160, but among a total of 7823 schools in the country. With this revised information, how many children in each school had a sandwich for lunch now?

Gemini-1.5 Flash:

Reasoning: To find the number of children per school who had a sandwich, we divide the total number of children who had a sandwich by the number of schools: 34160 children / 7823 schools = 4.37 children/school (rounded to two decimal places). 

Since we can't have a fraction of a child, we can say that approximately 4 children per school had a sandwich for lunch. 

### Answer: 4 

Expected answer: 34160/7823

Correct? No

Problem: Consider the previous toothpaste problem, but this time, the toothpaste tube contains 9060 grams of paste. How many times can you now brush your teeth with this tube of toothpaste if each brushing still uses an average of 306 grams?

Gemini-1.5 Flash:

Reasoning: We need to divide the total amount of toothpaste by the amount used per brushing: 9060 grams / 306 grams/brushing = 29.67 brushings. Since we can't have a fraction of a brushing, we round down to the nearest whole number.
### Answer: 29 

Expected answer: 1510/51

Correct? No

Problem: Now consider that the textile factory actually produced 8337 towels, still evenly distributed among 1309 boxes. How many towels are now in each box?

Gemini-1.5 Flash:

To find out how many towels are in each box, we need to divide the total number of towels by the number of boxes:

8337 towels / 1309 boxes = 6.37 towels/box

Since you can't have a fraction of a towel, we round down to the nearest whole number.

### Answer: 6 

Expected answer: 1191/187

Correct? No

Problem: Instead of 3318 Earth days, consider that the alien civilization uses a different form of time measurement, where each of their "days" represents 8212 of our Earth days. In this scenario, if they were still sending 43134 messages throughout this period, how many messages would they be sending per their "day"?

Gemini-1.5 Flash:

Here's how we can solve this:

* We know the aliens sent 43134 messages over a period that is equivalent to 3318 * 8212 = 27232796 Earth days.
* To find the number of messages sent per alien "day", we divide the total number of messages by the number of alien days: 43134 messages / 3318 alien days = 13 messages/alien day.

**Important Note:**  Even though the aliens use a different time measurement, they still send the same number of messages *per Earth day*. The time unit they use doesn't change the number of messages sent in a given amount of Earth time.  

### Answer: 13 

Expected answer: 21567/4106

Correct? No

Problem: The initial bus route was adjusted and the same 80,011 students are now equally distributed across 2069 buses due to a new policy. How many students are there per bus now?

Gemini-1.5 Flash:

To find out how many students are on each bus, we need to divide the total number of students by the number of buses. 

80,011 students / 2069 buses = 38.7 students per bus.  Since we can't have a fraction of a student, we round down to the nearest whole number.

### Answer: 38 

Expected answer: 80011/2069

Correct? No

Problem: After a successful marketing campaign, the camera store's sales increased, and they were able to sell 54020 cameras in just 5546 days. If they still sold the same number of cameras each day, how many cameras are now sold daily?

Gemini-1.5 Flash:

Reasoning: To find out the new daily sales, we divide the total number of cameras sold by the new number of days.

So, 54020 cameras / 5546 days = <<54020/5546=9.74 (approximately)>> 9.74 cameras per day (approximately).

Since we can't sell parts of a camera, we can say they sell approximately 10 cameras per day.

### Answer: 10 

Expected answer: 27010/2773

Correct? No

Problem: Instead of packing the 25774 liters of ice cream into 526 containers, the factory decides to use only 418 containers. If they divide the ice cream evenly among these containers, how many liters of ice cream does each container now accommodate?

Gemini-1.5 Flash:

Reasoning:  To find out how many liters each container holds when using 418 containers, we need to divide the total liters of ice cream by the new number of containers.
Each container now holds 25774/418 = <<25774/418=61.7>> 61.7 liters of ice cream.
### Answer: 61.7 

Expected answer: 12887/209

Correct? No

Problem: With the same fleet of 3412 buses, the city's public transportation system only logs a total of 3940 miles driven next week. If each bus shared the work evenly again, how many miles did each bus drive in this week?

Gemini-1.5 Flash:

Reasoning: To find the distance traveled by each bus, we divide the total distance by the number of buses: 3940 miles / 3412 buses = approximately 1.15 miles/bus.

### Answer: 1.15 

Expected answer: 985/853

Correct? No

Problem: If the same wind turbine instead generates a total of 5837 kilowatts of energy over the same 75 hours, how much energy does it now produce per hour?

Gemini-1.5 Flash:

We can follow the same logic as before, dividing the total energy by the number of hours:

Energy per hour = Total energy / Number of hours

Energy per hour = 5837 kilowatts / 75 hours

Energy per hour = 77.83 kilowatts/hour (rounded to two decimal places)

### Answer: 77.83 kilowatts/hour 

Expected answer: 5837/75

Correct? No

Problem: Suppose the baby's weight gain was recalculated over a span of 1651 days. If the total weight gain was still 3734 grams, what would be the average daily weight gain now?

Gemini-1.5 Flash:

We follow the same process as before, dividing the total weight gain by the new number of days:

Average daily gain = Total weight gain / Number of days
Average daily gain = 3734 grams / 1651 days
Average daily gain ≈ 2.26 grams/day

### Answer: 2.26 

Expected answer: 3734/1651

Correct? No

Problem: If the firefighter instead uses a different hose that releases the same total amount of water, 33,532 liters, but this time it's over 7,845 minutes, how many liters of water are released per minute with this hose?

Gemini-1.5 Flash:

Reasoning: To find out how many liters of water are released per minute, we need to divide the total amount of water released by the number of minutes it took.

So, we divide 33,532 liters by 7,845 minutes: 33,532 / 7,845 = 4.28 (rounded to two decimal places).

This means the hose releases approximately 4.28 liters of water per minute.

### Answer: 4.28 

Expected answer: 33532/7845

Correct? No

Problem: The farmer realizes that she miscalculated and she actually collected a total of 96,120 eggs but it was from 9,046 chickens, not 20. How many eggs did each chicken actually contribute?

Gemini-1.5 Flash:

We need to divide the total number of eggs by the actual number of chickens to find out how many eggs each chicken laid. 

So, we have 96,120 eggs / 9,046 chickens = approximately 10.63 eggs per chicken.

Since we can't have fractions of eggs, we can round this down to the nearest whole number.

### Answer: 10 

Expected answer: 48060/4523

Correct? No

Problem: Instead of 11458 millimeters of rain falling over 17 days, suppose now that 11458 millimeters of rain fell over 8513 days. How much rain does the town now receive each day if it rains the same amount every day?

Gemini-1.5 Flash:

Reasoning: To find the daily rainfall, we need to divide the total rainfall by the number of days. 
So, the town receives 11458 millimeters / 8513 days = <<11458/8513 = 1.346 (approximately)>> 1.346 millimeters of rain each day.

### Answer: 1.346 

Expected answer: 11458/8513

Correct? No

Problem: If the pen factory had instead produced 2526 pens in 547 hours under the same even-paced conditions, how many pens would have been produced each hour?

Gemini-1.5 Flash:

Reasoning: To find out how many pens were produced per hour, we divide the total number of pens by the number of hours. 

2526 pens / 547 hours = <<2526/547=4.62>>4.62 pens per hour.

Since we can't have fractions of pens, we round this number to the nearest whole number.  Therefore, the factory produced approximately 5 pens per hour.

### Answer: 5 

Expected answer: 2526/547

Correct? No

Problem: Initially a school decided to equally distribute 285 erasers among 19 classrooms. But later, the school received a donation and the total number of erasers increased to 4681. If these erasers are equally distributed among the same 19 classrooms, how many erasers does each classroom get now?

Gemini-1.5 Flash:

Reasoning:  We need to divide the total number of erasers (4681) by the number of classrooms (19) to find out how many erasers each classroom gets.

So, 4681 erasers / 19 classrooms = 246.37 erasers per classroom. Since we can't have fractions of erasers, each classroom would get 246 erasers.

### Answer: 246 

Expected answer: 4681/19

Correct? No

Problem: In the last problem, the penguin covered a distance of 41020 feet in 5 hours. Now, consider a situation where the penguin only covered a distance of 4325 feet in the same 5 hours. What would be the penguin's speed in feet per hour in this new scenario?

Gemini-1.5 Flash:

Reasoning: To find the penguin's speed, we need to divide the total distance traveled by the time taken. 

Speed = Distance / Time

Speed = 4325 feet / 5 hours

Speed = 865 feet per hour

### Answer: 865 

Expected answer: 865

Correct? Yes

Problem: Suppose instead the reservoir could hold 63360 gallons of water but now it's divided into 9999 equal sections. How many gallons of water does each section then hold?

Gemini-1.5 Flash:

To find out how many gallons each section holds, we need to divide the total capacity of the reservoir by the number of sections.

So, we have: 63360 gallons / 9999 sections = 6.336 gallons/section (approximately)

### Answer: 6.336 

Expected answer: 640/101

Correct? No

Problem: Suppose the TV channel decided to reduce the total minutes of advertisements. Now, over a 59-day period, they only broadcast a total of 5352 minutes of advertisements. What is the new average of advertisement minutes shown each day?

Gemini-1.5 Flash:

Reasoning: To find the new average, we divide the new total minutes of advertisements by the number of days.
This gives us 5352 minutes / 59 days = <<5352/59=90.7>>90.7 minutes per day.

### Answer: 90.7 

Expected answer: 5352/59

Correct? No

Problem: If the teacher, instead of marking 59748 marks, marked a total of 7117 marks distributed evenly over the same 1149 exam papers, how many marks would be in each exam paper now?

Gemini-1.5 Flash:

Reasoning: To find out how many marks are in each exam paper, we divide the total number of marks by the number of exam papers: 7117 marks / 1149 exam papers = 6.19 marks/exam paper. 

Since we can't have a fraction of a mark, we would round down to the nearest whole number.

### Answer: 6 

Expected answer: 7117/1149

Correct? No

Problem: Suppose the butterfly had instead spread a total of 9710 eggs across the same 359 flowers. How many eggs did she lay on each flower in this case?

Gemini-1.5 Flash:

Reasoning:  We need to divide the total number of eggs by the number of flowers to find out how many eggs were on each flower. So, we have 9710 eggs / 359 flowers = 27 eggs per flower.

### Answer: 27 

Expected answer: 9710/359

Correct? No

Problem: Suppose instead of 95038 pixels, the camera has only 2122 pixels and still divides them evenly into 61 rows. How many pixels would there be in each row now?

Gemini-1.5 Flash:

Reasoning: To find the number of pixels in each row, we divide the total number of pixels by the number of rows: 2122 pixels / 61 rows = 35 pixels/row.
### Answer: 35 

Expected answer: 2122/61

Correct? No

Problem: The same ice cream factory has adjusted their volume and now makes a total of 4660 cones over the same 53 day period. If production is still uniform, how many ice cream cones are they making each day now?

Gemini-1.5 Flash:

Reasoning:  To find the daily production, we divide the total number of cones by the number of days. 

So, the new daily production is 4660 / 53 = <<4660/53=88>> 88 cones.

### Answer: 88 

Expected answer: 4660/53

Correct? No

Problem: In another scenario, a different fireplace burns 8712 kilojoules of energy in 4 hours. Assuming it also burns energy at a constant rate, how much energy does this fireplace burn in one hour?

Gemini-1.5 Flash:

Reasoning: To find the energy burned in one hour, we divide the total energy burned by the number of hours: 8712 kilojoules / 4 hours = 2178 kilojoules/hour.

### Answer: 2178 kilojoules/hour 

Expected answer: 2178

Correct? Yes

Problem: Suppose instead of 51156 kilograms of snow, only 6407 kilograms of snow was available for the same 9 teams in the snowman-making competition. How much snow, in kilograms, would each team get to make their snowman now?

Gemini-1.5 Flash:

Reasoning: With 6407 kilograms of snow and 9 teams, each team would get 6407 kilograms / 9 teams = 711.89 kilograms (approximately).  Since we can't have fractions of kilograms of snow, we round down to the nearest whole number.

### Answer: 711 

Expected answer: 6407/9

Correct? No

Problem: Instead of the original 30 days, the workers actually took 3028 days to harvest a total of 56250 apples, harvesting the same number of apples every day. In light of this new information, how many apples were actually harvested each day?

Gemini-1.5 Flash:

Reasoning: To find out how many apples were harvested each day, we need to divide the total number of apples by the number of days. 
56250 apples / 3028 days = 18.57 apples per day (approximately).

### Answer: 18.57 

Expected answer: 28125/1514

Correct? No

Problem: Considering the baby from the previous problem, suppose now that she spoke her first word after being awake for a shorter time of 8741 seconds. Keeping our day duration constant at 1729 seconds, after how many days in this scenario did she speak her first word?

Gemini-1.5 Flash:

Reasoning: We need to divide the total awake time by the length of a day to find the number of days. This gives us 8741 seconds / 1729 seconds/day = 5 days. 

### Answer: 5 

Expected answer: 8741/1729

Correct? No

Problem: Now, imagine that the fashion designer decides to use the same total number of 33536 beads, but wants to distribute them uniformly over a larger number of sections. If they decides to spread these beads over 3206 different sections on the dress, how many beads will there be in each section?

Gemini-1.5 Flash:

To find out how many beads will be used for each section, we need to divide the total number of beads by the new number of sections.

So, we have 33536 beads / 3206 sections = 10.46 beads per section.

However, since you can't have a fraction of a bead, we need to round down to the nearest whole number. 

### Answer: 10 

Expected answer: 16768/1603

Correct? No

Problem: After the fire is controlled, a firefighter continues to spray 8749 gallons of water to cool down the area over the next 299 minutes. If the firefighter sprays the same amount of water every minute as before, how many gallons does he spray each minute now?

Gemini-1.5 Flash:

Reasoning: We already know the firefighter sprays 234 gallons each minute. This information doesn't change even though the amount of water sprayed to cool down the area is different.

### Answer: 234 

Expected answer: 673/23

Correct? No

Problem: After revising their design slightly, the company now finds that they will only need 6354 square inches of glass material to produce 6122 of the new model of windows. How many square inches of glass are now required for each of the new model windows?

Gemini-1.5 Flash:

Reasoning: To find out how much glass is needed for each window, we need to divide the total amount of glass by the number of windows: 6354 square inches / 6122 windows = 1.038 square inches/window (rounded to the nearest thousandth).
### Answer: 1.038 

Expected answer: 3177/3061

Correct? No

Problem: After practicing for a while, the frog now jumps a total of 9064 centimeters in the same 512 jumps. If the frog jumps the same distance each time, how many centimeters does the frog now jump per jump?

Gemini-1.5 Flash:

Reasoning:  To find the new distance per jump, we divide the new total distance by the number of jumps: 9064 centimeters / 512 jumps = 17.75 centimeters/jump.
### Answer: 17.75 

Expected answer: 1133/64

Correct? No

Problem: If instead of planting a total of 1392 flowers, the gardener planted a total of 7275 flowers evenly into the 116 pots, then how many flowers would there be in each pot now?

Gemini-1.5 Flash:

Reasoning: To find out how many flowers are in each pot, we need to divide the total number of flowers by the number of pots. 
So, 7275 flowers / 116 pots = <<7275/116=62.76>> 62.76 flowers per pot. Since we can't have a fraction of a flower, we round down to the nearest whole number. 

### Answer: 62 

Expected answer: 7275/116

Correct? No

Problem: Suppose instead of 9 weeks, it took the ice cream shop 4035 days to sell a total of 31,176 scoops of ice cream. How many scoops of ice cream did they sell each day?

Gemini-1.5 Flash:

Reasoning: To find the number of scoops sold each day, we divide the total number of scoops by the number of days.

31,176 scoops / 4035 days = 7.72 scoops per day (approximately).

Since we can't sell fractions of scoops, we can round this down to the nearest whole number.

### Answer: 7 

Expected answer: 10392/1345

Correct? No

Problem: What if the sanctuary in the previous problem had only 9,073 bananas instead of 88,508? How many bananas would each monkey get then, if they still had to be split evenly among the 406 monkeys?

Gemini-1.5 Flash:

To find out how many bananas each monkey gets with a smaller total, we divide the total number of bananas by the number of monkeys:

9,073 bananas / 406 monkeys = 22.35 bananas/monkey

Since we can't have a fraction of a banana, each monkey would receive **22 bananas**, and there would be some bananas left over. 

### Answer: 22 

Expected answer: 9073/406

Correct? No

Problem: The furniture maker later realizes that there was a mistake in the initial order, and the hotel owner actually only wanted 3774 table legs, with each table having 2 legs. With this corrected order, how many tables is the hotel owner actually ordering?

Gemini-1.5 Flash:

Reasoning: To find the number of tables, we divide the total number of table legs by the number of legs per table. 
So, the hotel owner is actually ordering 3774 / 2 = <<3774/2 = 1887>> tables.
### Answer: 1887 

Expected answer: 1887

Correct? Yes

Problem: In the previous scenario, suppose the hat maker did not have 3560 feathers, but only had 1416 feathers instead. If each hat will still have 890 feathers, how many hats can be produced now?

Gemini-1.5 Flash:

Reasoning: We know each hat needs 890 feathers, and we only have 1416 feathers. To find out how many hats can be made, we need to divide the total feathers we have by the number of feathers per hat: 1416 / 890. However, we cannot make a complete hat with less than 890 feathers. So, we need to find the largest whole number that is less than the result of this division.

Since 1416/890 is slightly greater than 1, we can only make **one** complete hat.

### Answer: 1 

Expected answer: 708/445

Correct? No

Problem: Now, consider a similar game where the total of 17394 points is now distributed evenly among 7489 players instead. In this case, how many points would each player have?

Gemini-1.5 Flash:

Reasoning: To find out how many points each player has, we divide the total points by the number of players: 17394 / 7489 = <<17394 / 7489 = 2.32>>. Since we can't have a fraction of a point, we round down. 
### Answer: 2 

Expected answer: 17394/7489

Correct? No

Problem: If instead of the original size, the park was smaller, covering only 139 acres, but the sections remained the same, each with an equal area, how many acres would each section cover?

Gemini-1.5 Flash:

If the park covers 139 acres and is divided into 126 sections, each section would cover:

139 acres / 126 sections = 1.10317460317 acres/section

Since we're dealing with real-world measurements, it makes sense to round this to a more practical number:

### Answer: 1.1 acres 

Expected answer: 139/126

Correct? No

Problem: The pants manufacturer now only has 4769 yards of fabric left. If they still plan on making 11 pairs of pants with this fabric, and each pair will still consume an equal portion of the total fabric, how many yards of fabric are needed for each pair now?

Gemini-1.5 Flash:

Reasoning: If the pants manufacturer wants to make 11 pairs of pants with 4769 yards of fabric, each pair will need 4769/11 = <<4769/11=433.55>>433.55 yards of fabric. 
### Answer: 433.55 

Expected answer: 4769/11

Correct? No

Problem: Considering that the minute hand of the clock actually rotates 49716 degrees throughout 9706 hours instead of 18, how many degrees does it rotate each hour?

Gemini-1.5 Flash:

Reasoning: The minute hand of a clock rotates 49716/9706 = <<49716/9706=5.12 (rounded to two decimal places)>> 5.12 degrees each hour.
### Answer: 5.12 

Expected answer: 24858/4853

Correct? No

Problem: In an alternate scenario, the toy company made 2542 stuffed animals, still spread over 373 different designs. If each design had the same number of stuffed animals in this scenario, how many stuffed animals would there be for each design?

Gemini-1.5 Flash:

Reasoning: To find the number of stuffed animals per design, we divide the total number of stuffed animals by the number of designs: 2542 stuffed animals / 373 designs = 6.8 stuffed animals per design. Since we cannot have fractions of stuffed animals, we round this number down to the nearest whole number. 
### Answer: 6 

Expected answer: 2542/373

Correct? No

Problem: Considering our previous calculation, if a bear travels a total of 31470 feet but this time over 1406 days instead of 30 days and still travels the same distance each day, how many feet does it travel each day now?

Gemini-1.5 Flash:

Reasoning: To find the distance the bear travels each day, we need to divide the total distance by the number of days. 

So, the bear travels 31470 feet / 1406 days = <<31470/1406=22.4>>22.4 feet each day.

### Answer: 22.4 

Expected answer: 15735/703

Correct? No