Problem: Carla has a garden and wants to calculate the amount of cucumbers she will be able to grow. She noticed that the number of cucumbers she could grow per plant was determined by multiplying 22/3 by 22/19. After a few months, she realized that she could grow her production by multiplying the initial amount by 23/17. How many cucumbers is she expecting to grow per plant after adjusting her production method?

Claude-3 Sonnet:

To solve this problem, we need to find the initial number of cucumbers per plant and then multiply it by the adjustment factor (23/17).

Given information:
- The initial number of cucumbers per plant is determined by multiplying 22/3 by 22/19.
- The production is adjusted by multiplying the initial amount by 23/17.

Step 1: Find the initial number of cucumbers per plant.
Initial number of cucumbers per plant = (22/3) × (22/19)
Initial number of cucumbers per plant = (484/57)
Initial number of cucumbers per plant = 8.49 (approximately)

Step 2: Find the adjusted number of cucumbers per plant.
Adjusted number of cucumbers per plant = Initial number of cucumbers per plant × (23/17)
Adjusted number of cucumbers per plant = 8.49 × (23/17)
Adjusted number of cucumbers per plant = 11.47 (approximately)

Therefore, after adjusting her production method, Carla is expecting to grow approximately 11.47 cucumbers per plant.

### Answer: 11.47

Expected answer: 11132/969

Correct? No

Problem: Pierre has 19/4 kg of grapes. One afternoon, he ate 7/25 kg of them. In the evening, his mother gave him 30/9 kg more grapes. How many kilograms of grapes does Pierre have now?

Claude-3 Sonnet:

To solve this problem, we need to find the total amount of grapes Pierre has after eating some and receiving more from his mother.

Given information:
- Pierre initially had 19/4 kg of grapes.
- He ate 7/25 kg of grapes in the afternoon.
- His mother gave him 30/9 kg more grapes in the evening.

Step 1: Convert the fractions to equivalent fractions with a common denominator.
19/4 = (19 × 25)/100 = 475/100 kg
7/25 = 7/25 kg
30/9 = (30 × 25)/225 = 750/225 kg

Step 2: Find the amount of grapes Pierre had after eating some.
Initial amount of grapes - Amount eaten = Amount remaining
475/100 kg - 7/25 kg = (475/100 - 28/100) kg = 447/100 kg

Step 3: Find the total amount of grapes Pierre has now after receiving more from his mother.
Amount remaining + Amount received = Total amount
447/100 kg + 750/225 kg = (447 × 225 + 750 × 100) / (100 × 225) kg
                         = 100,575/22,500 kg
                         = 4.47 kg

Therefore, Pierre now has 4.47 kg of grapes.

### Answer: 4.47

Expected answer: 2341/300

Correct? No

Problem: King Arthur is calculating the costs for restoring his castle. The wall repairs cost 26/22 of his castle's annual budget. Meanwhile, the moat renovations cost an additional 4/29 of the budget. Finally, installing new defensive catapults takes up an 11/3 portion of the budget. How much (expressed as a fraction of the castle's annual budget) has King Arthur spent on these projects in total?

Claude-3 Sonnet:

To solve this problem, we need to add the fractions representing the costs of each project.

Given information:
- Wall repairs cost 26/22 of the castle's annual budget.
- Moat renovations cost 4/29 of the budget.
- Installing new defensive catapults takes up 11/3 of the budget.

Step 1: Find the least common denominator (LCD) for all the fractions.
LCD = 462 (the least common multiple of 22, 29, and 3)

Step 2: Convert all fractions to equivalent fractions with the LCD as the denominator.
Wall repairs cost = (26/22) × (21/21) = 546/462
Moat renovations cost = (4/29) × (16/16) = 64/462
Installing new defensive catapults cost = (11/3) × (154/154) = 1694/462

Step 3: Add the fractions.
Total cost = (546/462) + (64/462) + (1694/462)
            = 2304/462

Step 4: Simplify the fraction if possible.
2304/462 = 5 (by dividing both the numerator and denominator by 462)

Therefore, King Arthur has spent 5 portions of the castle's annual budget on these projects in total.

### Answer: 5

Expected answer: 4772/957

Correct? No

Problem: A giraffe at the local zoo has a peculiar eating habit. When it is fed 25/19 lbs of acacia leaves, it eats 30/26 times more than what it usually does in a day. If the zoo calculates the weekly feeding amount by multiplying the daily intake by itself (making the result "weekly feeding amount squared") and then multiplying that with the regular daily intake, how many pounds of acacia leaves should they prepare for the giraffe for a week? Calculate ((25 / 19) * (30 / 26))^2 * ((25 / 19) * (30 / 26)) and provide your answer.

Claude-3 Sonnet:

To solve this problem, we need to follow the given steps and perform the required calculations.

Given information:
- The giraffe eats 25/19 lbs of acacia leaves, which is 30/26 times more than its usual daily intake.
- The weekly feeding amount is calculated by multiplying the daily intake by itself (squaring it) and then multiplying that with the regular daily intake.

Step 1: Calculate the daily intake of the giraffe.
Daily intake = (25/19) * (30/26)
Daily intake = (25 * 30) / (19 * 26)
Daily intake = 750 / 494
Daily intake = 1.518 lbs

Step 2: Calculate the weekly feeding amount squared.
Weekly feeding amount squared = (Daily intake)^2
Weekly feeding amount squared = (1.518)^2
Weekly feeding amount squared = 2.304

Step 3: Calculate the weekly feeding amount by multiplying the weekly feeding amount squared with the daily intake.
Weekly feeding amount = Weekly feeding amount squared * Daily intake
Weekly feeding amount = 2.304 * 1.518
Weekly feeding amount = 3.499 lbs

Therefore, the zoo should prepare 3.499 lbs of acacia leaves for the giraffe for a week.

### Answer: 3.499

Expected answer: 52734375/15069223

Correct? No

Problem: Lara wants to make a necklace. The necklace requires (11/3) feet of yarn. She also wants to add smaller beads which will extend the length of the necklace by (8/30) feet. How many feet of materials will Lara need to make the necklace?

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the length of yarn required for the necklace and the additional length due to the smaller beads.

Given information:
- The necklace requires (11/3) feet of yarn.
- The smaller beads will extend the length of the necklace by (8/30) feet.

Step 1: Convert the fractions to equivalent fractions with a common denominator.
(11/3) = (110/30) feet of yarn
(8/30) feet for the smaller beads

Step 2: Add the lengths together.
Length of yarn + Length of smaller beads = Total length of materials needed
(110/30) + (8/30) = 118/30 feet

Step 3: Convert the fraction to a mixed number or decimal form for better understanding.
118/30 = 3 (28/30) feet
118/30 = 3.93 feet

Therefore, Lara will need 3.93 feet or 3 (28/30) feet of materials to make the necklace.

### Answer: 3.93 feet

Expected answer: 59/15

Correct? No

Problem: Two planes depart from an airport at the exact same time. Plane A is flying at a speed of 24/11 miles per minute and Plane B is flying at a speed of 26/27 miles per minute. How much farther (in miles) did Plane A travel than Plane B after exactly one minute, assuming they keep flying at a stable speed? Calculate the difference and write your answer as a simplified fraction.

Claude-3 Sonnet:

To solve this problem, we need to find the distance traveled by each plane after one minute and then calculate the difference between them.

Given information:
- Plane A is flying at a speed of 24/11 miles per minute.
- Plane B is flying at a speed of 26/27 miles per minute.

Step 1: Find the distance traveled by Plane A after one minute.
Distance traveled by Plane A = Speed of Plane A × Time
Distance traveled by Plane A = (24/11) miles per minute × 1 minute
Distance traveled by Plane A = 24/11 miles

Step 2: Find the distance traveled by Plane B after one minute.
Distance traveled by Plane B = Speed of Plane B × Time
Distance traveled by Plane B = (26/27) miles per minute × 1 minute
Distance traveled by Plane B = 26/27 miles

Step 3: Calculate the difference between the distances traveled by Plane A and Plane B.
Difference = Distance traveled by Plane A - Distance traveled by Plane B
Difference = (24/11) - (26/27) miles

To find the difference, we need to find a common denominator for the fractions.
The least common multiple of 11 and 27 is 297.

(24/11) = (24 × 27/297)
(24/11) = 648/297

(26/27) = (26 × 11/297)
(26/27) = 286/297

Difference = (648/297) - (286/297)
Difference = 362/297 miles

To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator.
The GCF of 362 and 297 is 1.

Therefore, the simplified fraction is 362/297.

### Answer: 362/297

Expected answer: 362/297

Correct? Yes

Problem: In the wild, an adult bear eats about 14/7 pounds of fish per day. A young bear eats about 25/13 pounds of fish per day. Calculate the combined amount that both bears eat per day by multiplying 14/7 by 25/13.

Claude-3 Sonnet:

To calculate the combined amount that both bears eat per day, we need to multiply 14/7 by 25/13.

First, we need to find a common denominator for the fractions 14/7 and 25/13. The least common multiple of 7 and 13 is 91.

So, we convert the fractions to equivalent fractions with a denominator of 91:
14/7 = (14 × 13)/91 = 182/91
25/13 = (25 × 7)/91 = 175/91

Now, we can multiply the fractions:
(182/91) × (175/91) = (182 × 175) / (91 × 91) = 31,850 / 8,281 = 3.845...

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 11.
31,850 / 11 = 2,895
8,281 / 11 = 753

Therefore, the combined amount that both bears eat per day is 2,895/753 pounds of fish.

### Answer: 2,895/753

Expected answer: 50/13

Correct? No

Problem: Toby plays guitar. His first song takes 12/8 hours to play and his second song takes 12/3 hours to play. How long does it take Toby to play both of his songs? Write your answer as a simplified fraction.

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the times it takes Toby to play each song, and then simplify the resulting fraction.

Given information:
- Toby's first song takes 12/8 hours to play.
- Toby's second song takes 12/3 hours to play.

Step 1: Find the least common denominator (LCD) of 8 and 3.
The LCD of 8 and 3 is 24.

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
12/8 hours = (12/8) × (3/3) = 36/24 hours
12/3 hours = (12/3) × (8/8) = 96/24 hours

Step 3: Add the fractions.
(36/24) + (96/24) = 132/24 hours

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
The GCF of 132 and 24 is 12.
132/24 = (132/12) / (24/12) = 11/2 hours

Therefore, it takes Toby 11/2 hours to play both of his songs.

### Answer: 11/2

Expected answer: 11/2

Correct? Yes

Problem: Suppose you have 28 out of 29 chocolate bars. Then, you found 8 out of 22 more chocolate bars. What fraction represents the total chocolate bars you have now?

Claude-3 Sonnet:

To solve this problem, we need to find the total number of chocolate bars and then express it as a fraction over the total number of chocolate bars available.

Given information:
- Initially, you have 28 out of 29 chocolate bars.
- You found 8 out of 22 more chocolate bars.

Step 1: Find the total number of chocolate bars you have now.
Number of chocolate bars initially = 28
Number of chocolate bars found = 8
Total number of chocolate bars = 28 + 8 = 36

Step 2: Find the total number of chocolate bars available.
Total number of chocolate bars available = 29 + 22 = 51

Step 3: Express the total chocolate bars you have now as a fraction.
Fraction of chocolate bars you have now = Total number of chocolate bars you have / Total number of chocolate bars available
Fraction of chocolate bars you have now = 36 / 51

Therefore, the fraction that represents the total chocolate bars you have now is 36/51.

### Answer: 36/51

Expected answer: 424/319

Correct? No

Problem: A compass maker is creating some specialty compasses. The compass needle is made from a special material. It takes 27/26 of a pound to create one needle. If the maker is trying to produce two identical needles, how much material will he require? After producing the two needles, the maker realizes he needs to produce an additional piece for the compass that requires 27/6 pounds of the material. How much total material will the compass maker need to produce the two needles and the additional piece?

Claude-3 Sonnet:

To solve this problem, we need to find the amount of material required for two needles and then add the amount required for the additional piece.

Given information:
- It takes 27/26 pounds of material to create one needle.
- The maker needs to produce two identical needles.
- The additional piece requires 27/6 pounds of material.

Step 1: Find the amount of material required for two needles.
Amount of material for one needle = 27/26 pounds
Amount of material for two needles = 2 × (27/26) pounds
Amount of material for two needles = 54/26 pounds

Step 2: Find the total amount of material required for two needles and the additional piece.
Total amount of material = Amount of material for two needles + Amount of material for the additional piece
Total amount of material = (54/26) pounds + (27/6) pounds
Total amount of material = (54/26 + 135/26) pounds
Total amount of material = 189/26 pounds

Therefore, the compass maker will need a total of 189/26 pounds of material to produce the two needles and the additional piece.

### Answer: 189/26

Expected answer: 171/26

Correct? No

Problem: Liam bought a candle that burns at a rate of 6/4 inches per hour. After some time, he bought another candle that burns at a slower rate of 14/16 inches per hour. What is the total rate at which the two candles burn together?

Claude-3 Sonnet:

To solve this problem, we need to find the rate at which each candle burns and then add them together.

Given information:
- The first candle burns at a rate of 6/4 inches per hour.
- The second candle burns at a rate of 14/16 inches per hour.

Step 1: Convert the rates to a common denominator.
Rate of the first candle = (6/4) × (4/4) = 6/4 inches per hour
Rate of the second candle = (14/16) × (4/4) = 7/8 inches per hour

Step 2: Add the rates together.
Total rate = Rate of the first candle + Rate of the second candle
Total rate = 6/4 + 7/8 inches per hour
Total rate = (6/4 × 8/8) + (7/8 × 4/4) inches per hour
Total rate = 48/32 + 28/32 inches per hour
Total rate = 76/32 inches per hour

Step 3: Simplify the fraction if possible.
76/32 = 19/8 inches per hour

Therefore, the total rate at which the two candles burn together is 19/8 inches per hour.

### Answer: 19/8

Expected answer: 19/8

Correct? Yes

Problem: Sophia has 17/20 of a dollar. Her friend gives her another 1/4 of a dollar. After some time, her brother gives her 1 dollar. How much money does Sophia have now in dollars?

Claude-3 Sonnet:

To solve this problem, we need to convert the fractions to decimals and then add them together.

Given information:
- Sophia has 17/20 of a dollar.
- Her friend gives her 1/4 of a dollar.
- Her brother gives her 1 dollar.

Step 1: Convert 17/20 to a decimal.
17/20 = 0.85

Step 2: Convert 1/4 to a decimal.
1/4 = 0.25

Step 3: Add the amounts together.
Sophia's initial amount = 0.85 dollars
Amount given by her friend = 0.25 dollars
Amount given by her brother = 1.00 dollar
Total amount = 0.85 + 0.25 + 1.00 = 2.10 dollars

Therefore, Sophia has 2.10 dollars now.

### Answer: 2.10

Expected answer: 21/10

Correct? Yes

Problem: Imagine you're a music producer who is working on a new song. Your resources are divided into different sections. - First, you dedicate 16/4 hours to composing the music and another 16/29 hours to writing the lyrics. This is your initial time investment for the song (let's call it p). - Then, you spend 28/13 hours for mixing and mastering the song in addition to the initial time investment (let's call this new total time b). - Suddenly, a drummer you hired for a session uses 18/4 hours less because he finished his parts quickly. What is the final time you spent on producing the song, if your total time is expressed as (b - (18 / 4))?

Claude-3 Sonnet:

To solve this problem, we need to find the values of p and b, and then calculate the final time spent on producing the song using the given expression (b - (18 / 4)).

Given information:
- Initial time investment for composing the music and writing the lyrics (p) = 16/4 + 16/29 hours.
- Total time including mixing and mastering (b) = Initial time investment (p) + 28/13 hours.
- The drummer used 18/4 hours less than expected.

Step 1: Find the value of p (initial time investment).
p = 16/4 + 16/29
p = 4 + 0.5517... (approximately)
p ≈ 4.552 hours

Step 2: Find the value of b (total time including mixing and mastering).
b = p + 28/13
b = 4.552 + 2.1538...
b ≈ 6.706 hours

Step 3: Calculate the final time spent on producing the song using the given expression (b - (18 / 4)).
Final time = b - (18 / 4)
Final time = 6.706 - 4.5
Final time ≈ 2.206 hours

Therefore, the final time you spent on producing the song is approximately 2.206 hours.

### Answer: 2.206

Expected answer: 1663/754

Correct? No

Problem: Monica has 21/15 dozens of cookies at her bakery shop. Later in the day, she bakes additional 29/17 dozens of cookies to add into her stock. At the end of the day, she decides to increase her total stock of cookies by a ratio of 7/5 for an upcoming cookie festival. How many dozens of cookies will Monica have for the cookie festival?

Claude-3 Sonnet:

To solve this problem, we need to find the total number of dozens of cookies Monica has after baking the additional cookies, and then multiply it by the ratio 7/5 to find the final number of dozens of cookies for the cookie festival.

Given information:
- Monica initially has 21/15 dozens of cookies.
- She bakes an additional 29/17 dozens of cookies.
- She wants to increase her total stock of cookies by a ratio of 7/5 for the cookie festival.

Step 1: Convert the mixed fractions to improper fractions.
21/15 dozens = (21 × 1 + 0)/15 = 21/15 dozens
29/17 dozens = (29 × 1 + 0)/17 = 29/17 dozens

Step 2: Find the total number of dozens of cookies after baking the additional cookies.
Total dozens of cookies = Initial dozens of cookies + Additional dozens of cookies
Total dozens of cookies = 21/15 + 29/17
Total dozens of cookies = (21 × 17 + 29 × 15) / (15 × 17)
Total dozens of cookies = 357 / 255 + 435 / 255
Total dozens of cookies = 792 / 255

Step 3: Increase the total stock of cookies by the ratio of 7/5.
Final dozens of cookies = (Total dozens of cookies) × (7/5)
Final dozens of cookies = (792 / 255) × (7/5)
Final dozens of cookies = (792 × 7) / (255 × 5)
Final dozens of cookies = 5544 / 1275
Final dozens of cookies = 4.35 dozens (rounded to two decimal places)

### Answer: 4.35

Expected answer: 1848/425

Correct? No

Problem: In a bakery, a certain cake recipe requires 26/24 kg of sugar per cake. If a chef starts with 28 kg of sugar, how many kilograms of sugar will they have left after making one cake and then adding 10/6 kg of sugar to their supply?

Claude-3 Sonnet:

To solve this problem, we need to find the amount of sugar used for one cake and then subtract it from the initial amount of sugar. After that, we need to add the additional sugar to the remaining amount.

Given information:
- The cake recipe requires 26/24 kg of sugar per cake.
- The chef starts with 28 kg of sugar.
- After making one cake, the chef adds 10/6 kg of sugar to their supply.

Step 1: Convert the fractions to decimals.
26/24 kg = 1.083 kg of sugar per cake
10/6 kg = 1.667 kg of additional sugar

Step 2: Find the amount of sugar used for one cake.
Amount of sugar used for one cake = 1.083 kg

Step 3: Find the remaining amount of sugar after making one cake.
Remaining sugar = Initial sugar - Sugar used for one cake
Remaining sugar = 28 kg - 1.083 kg = 26.917 kg

Step 4: Find the total amount of sugar after adding the additional sugar.
Total sugar = Remaining sugar + Additional sugar
Total sugar = 26.917 kg + 1.667 kg = 28.584 kg

Therefore, after making one cake and adding 10/6 kg of sugar to their supply, the chef will have 28.584 kg of sugar left.

### Answer: 28.584

Expected answer: 343/12

Correct? No

Problem: On a plane trip, Emily watched a total of 16 / 4 hours of movies. During this time, she spent 6 / 3 hours watching a comedy film. How many hours did she spend watching movies other than the comedy film?

Claude-3 Sonnet:

To solve this problem, we need to find the difference between the total time Emily spent watching movies and the time she spent watching the comedy film.

Given information:
- Emily watched a total of 16 / 4 = 4 hours of movies.
- Emily spent 6 / 3 = 2 hours watching a comedy film.

Step 1: Find the time spent watching movies other than the comedy film.
Time spent watching other movies = Total time watching movies - Time spent watching the comedy film
Time spent watching other movies = 4 hours - 2 hours
Time spent watching other movies = 2 hours

Therefore, Emily spent 2 hours watching movies other than the comedy film.

### Answer: 2

Expected answer: 2

Correct? Yes

Problem: Princess Lily was dining at a finely set table and in front of her, two dishes were placed, one with slices of apple pie and the other with slices of blueberry pie. She can eat pie slices endlessly! She ate 10 out of the 12 slices of the apple pie and 10 out of the 29 slices of the blueberry pie. How much of the pies (combined) did she eat? Represent your answer as a fraction.

Claude-3 Sonnet:

To solve this problem, we need to find the total number of pie slices and the number of slices Lily ate, and then represent the fraction of pies she ate.

Given information:
- There were 12 slices of apple pie, and Lily ate 10 slices.
- There were 29 slices of blueberry pie, and Lily ate 10 slices.

Step 1: Find the total number of pie slices.
Total number of pie slices = Number of apple pie slices + Number of blueberry pie slices
Total number of pie slices = 12 + 29 = 41 slices

Step 2: Find the number of pie slices Lily ate.
Number of pie slices Lily ate = Number of apple pie slices eaten + Number of blueberry pie slices eaten
Number of pie slices Lily ate = 10 + 10 = 20 slices

Step 3: Represent the fraction of pies Lily ate.
Fraction of pies Lily ate = Number of pie slices Lily ate / Total number of pie slices
Fraction of pies Lily ate = 20 / 41

### Answer: 20/41

Expected answer: 205/174

Correct? No

Problem: Marta has a box of colored pencils. She uses 20 of the colored pencils every 11 days on her art projects. However, she only uses about 23 out of every 26 colored pencils for shading techniques. How many colored pencils does Marta use for shading in her art projects over an 11-day period? Evaluate by performing the operation (20 / 11) * (23 / 26) and write your answer as a simplified fraction.

Claude-3 Sonnet:

To solve this problem, we need to find the number of colored pencils Marta uses for shading in her art projects over an 11-day period.

Given information:
- Marta uses 20 colored pencils every 11 days.
- Marta uses about 23 out of every 26 colored pencils for shading techniques.

Step 1: Find the fraction of colored pencils Marta uses for shading in an 11-day period.
Fraction of colored pencils used for shading = (20 / 11) × (23 / 26)

Step 2: Perform the multiplication of fractions.
(20 / 11) × (23 / 26) = (20 × 23) / (11 × 26)
= 460 / 286

Step 3: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.
GCF of 460 and 286 = 2

Step 4: Divide the numerator and denominator by the GCF.
460 / 2 = 230
286 / 2 = 143

Therefore, the simplified fraction representing the number of colored pencils Marta uses for shading in her art projects over an 11-day period is:

### Answer: 230/143

Expected answer: 230/143

Correct? Yes

Problem: A police investigator is analyzing two evidence specimens. The first specimen has a unique property that decreases its value by 26 out of every 6 units. The second specimen decreases its value by 25 out of every 17 units. The investigator needs to find the ratio of these changes, referred to as indicator i. Additionally, he needs to figure out a set of changes in another pair of evidence specimens. The first one of this pair increases its value by 18 out of every 8 units and the second one increases its value by 17 out of every 23 units. The investigator has to find the difference between these two rates and refer to it as indicator h. He then combines these two indicators (h and i) by multiplying them to get a final evidence factor, referred to as indicator f. This will help determine the likelihood of a particular suspect’s involvement. Calculate the value of f.

Claude-3 Sonnet:

To solve this problem, we need to find the values of indicators i and h, and then calculate their product to get indicator f.

Given information:
- The first specimen decreases its value by 26 out of every 6 units.
- The second specimen decreases its value by 25 out of every 17 units.
- The first specimen of the second pair increases its value by 18 out of every 8 units.
- The second specimen of the second pair increases its value by 17 out of every 23 units.

Step 1: Find the ratio of the changes in the first pair of specimens (indicator i).
Ratio of change for the first specimen = 26/6 = 4.33
Ratio of change for the second specimen = 25/17 ≈ 1.47
Indicator i = Ratio of change for the first specimen / Ratio of change for the second specimen
Indicator i = 4.33 / 1.47 ≈ 2.94

Step 2: Find the difference between the rates of change in the second pair of specimens (indicator h).
Rate of change for the first specimen = 18/8 = 2.25
Rate of change for the second specimen = 17/23 ≈ 0.74
Indicator h = Rate of change for the first specimen - Rate of change for the second specimen
Indicator h = 2.25 - 0.74 = 1.51

Step 3: Calculate the final evidence factor (indicator f) by multiplying indicators i and h.
Indicator f = Indicator i × Indicator h
Indicator f = 2.94 × 1.51 ≈ 4.44

Therefore, the final evidence factor (indicator f) is approximately 4.44.

### Answer: 4.44

Expected answer: 30719/6900

Correct? No

Problem: In a wildlife park, there are lions and giraffes. During one particular year, the gestation period of a lioness is represented as 20/22 of a year, while a giraffe's gestation period is 15 years. Find the total gestation period of both animals together. Later in the same year, a lioness is pregnant again but this time her gestation period reduces by 15/20 of a year compared to the earlier total gestation period of both animals. How long will it take for the lioness to give birth this second time?

Claude-3 Sonnet:

To solve this problem, we need to find the total gestation period of both animals together and then calculate the reduced gestation period for the lioness in the second pregnancy.

Given information:
- The gestation period of a lioness is 20/22 of a year.
- The gestation period of a giraffe is 15 years.
- In the second pregnancy, the lioness's gestation period reduces by 15/20 of the earlier total gestation period of both animals.

Step 1: Find the total gestation period of both animals together.
Gestation period of a lioness = 20/22 years
Gestation period of a giraffe = 15 years
Total gestation period = Gestation period of a lioness + Gestation period of a giraffe
Total gestation period = 20/22 + 15 years
Total gestation period = (20/22 + 330/22) years (converting 15 years to 330/22 years)
Total gestation period = 350/22 years

Step 2: Calculate the reduced gestation period for the lioness in the second pregnancy.
Reduction in gestation period = 15/20 of the earlier total gestation period
Reduction in gestation period = (15/20) × (350/22) years
Reduction in gestation period = 105/44 years

New gestation period for the lioness = Earlier gestation period - Reduction in gestation period
New gestation period for the lioness = 20/22 years - 105/44 years
New gestation period for the lioness = (440/484 - 105/484) years
New gestation period for the lioness = 335/484 years

Therefore, it will take 335/484 years (approximately 0.692 years or 8.3 months) for the lioness to give birth in the second pregnancy.

### Answer: 335/484

Expected answer: 667/44

Correct? No

Problem: A rectangle's length is 30/7 meters and its width is 19/6 meters. The area of the rectangle is found by multiplying the length and the width. If a similar rectangle has an area which is 18/17 times bigger than the original rectangle, what is the area of the similar rectangle?

Claude-3 Sonnet:

To solve this problem, we need to find the area of the original rectangle and then use the given ratio to find the area of the similar rectangle.

Given information:
- The length of the original rectangle is 30/7 meters.
- The width of the original rectangle is 19/6 meters.
- The area of the similar rectangle is 18/17 times bigger than the area of the original rectangle.

Step 1: Find the area of the original rectangle.
Area of the original rectangle = Length × Width
Area of the original rectangle = (30/7) × (19/6)
Area of the original rectangle = (30 × 19) / (7 × 6)
Area of the original rectangle = 570 / 42
Area of the original rectangle = 13.57 square meters

Step 2: Find the area of the similar rectangle.
Area of the similar rectangle = Area of the original rectangle × (18/17)
Area of the similar rectangle = 13.57 × (18/17)
Area of the similar rectangle = 244.26 / 17
Area of the similar rectangle = 14.37 square meters

Therefore, the area of the similar rectangle is 14.37 square meters.

### Answer: 14.37

Expected answer: 1710/119

Correct? No

Problem: A soap factory produces 23/8 tonnes of soap each day. One day, they decided to increase production by an extra 4/20 of a tonne. However, later that same day, they reduce the production by 19/24 of a tonne due to a sudden power cut. How many tonnes of soap does the factory produce that day after these adjustments?

Claude-3 Sonnet:

To solve this problem, we need to find the initial production, then add the increase and subtract the reduction.

Given information:
- The factory produces 23/8 tonnes of soap each day.
- They increased production by an extra 4/20 of a tonne.
- They reduced production by 19/24 of a tonne due to a power cut.

Step 1: Convert the fractions to a common denominator.
Initial production = 23/8 tonnes = (23 × 3)/24 = 69/24 tonnes
Increase in production = 4/20 tonnes = (4 × 6)/120 = 24/120 tonnes
Reduction in production = 19/24 tonnes

Step 2: Add the increase to the initial production.
Production after increase = 69/24 + 24/120 = (69 × 5 + 24)/120 = 369/120 tonnes

Step 3: Subtract the reduction from the production after increase.
Final production = 369/120 - 19/24 = (369/120 - 19/30) = (369 - 57)/120 = 312/120 tonnes

Step 4: Convert the final production to a mixed number.
312/120 = 2 60/120 = 2 1/2 tonnes

### Answer: 2 1/2

Expected answer: 137/60

Correct? No

Problem: You have a paint mixing machine that creates specific shades of color. The machine starts by mixing 24/8 gallons of red paint. It then pours away 12/8 gallons of the mix. Let 'd' represent the amount of red paint left in the machine. Finally, the machine adds another 1/28 gallon of blue pigment to lighten the color, subtract that from 'd' to find 'x' in gallons, which is the total amount of paint. Find the value of 'x'.

Claude-3 Sonnet:

To solve this problem, we need to follow the given steps and perform the necessary calculations.

Given information:
- The machine starts by mixing 24/8 = 3 gallons of red paint.
- It then pours away 12/8 = 1.5 gallons of the mix.
- Let 'd' represent the amount of red paint left in the machine.
- The machine adds another 1/28 gallon of blue pigment to lighten the color.
- 'x' is the total amount of paint after adding the blue pigment.

Step 1: Find the amount of red paint left in the machine after pouring away 1.5 gallons.
Amount of red paint left = Initial amount of red paint - Amount poured away
d = 3 gallons - 1.5 gallons
d = 1.5 gallons

Step 2: Find the total amount of paint 'x' after adding the blue pigment.
x = Amount of red paint left + Amount of blue pigment added
x = 1.5 gallons + 1/28 gallon
x = 1.5 gallons + (1/28) × (1/4) gallon (Converting 1/28 to a fraction of a gallon)
x = 1.5 gallons + 0.0089 gallon
x = 1.5089 gallons

Therefore, the total amount of paint 'x' after adding the blue pigment is 1.5089 gallons.

### Answer: 1.5089

Expected answer: 41/28

Correct? No

Problem: A banana bread recipe requires you to multiply the fractions (27 / 14) and (17 / 13) together to determine how many ounces of mashed bananas you'll need. Compute the product of these fractions and write your answer as a simplified fraction to find out how many ounces are required.

Claude-3 Sonnet:

To multiply two fractions, we multiply the numerators together and the denominators together.

(27/14) x (17/13)
= (27 x 17) / (14 x 13)
= 459 / 182

To simplify the fraction 459/182, we need to find the greatest common factor (GCF) of 459 and 182, and then divide both the numerator and denominator by the GCF.

The GCF of 459 and 182 is 7.
459 / 7 = 65
182 / 7 = 26

Therefore, the simplified fraction is 65/26.

### Answer: 65/26

Expected answer: 459/182

Correct? No

Problem: Sonia uses 21/12 oz of toothpaste to brush her teeth every day. Her brother Anthony uses less toothpaste, just 6/27 oz daily. Add both quantities of toothpaste to get the total daily amount used by Sonia and Anthony. Now, suppose their mom includes an amount of toothpaste for herself to the total - she uses 3/18 oz of toothpaste daily. Add this amount to the total used by Sonia and Anthony to get the final total daily toothpaste usage for the whole family. Solve each fraction separately and give the answer as a simplified fraction.

Claude-3 Sonnet:

To solve this problem, we need to find a common denominator for all the fractions involved, and then add the numerators.

Given information:
- Sonia uses 21/12 oz of toothpaste daily.
- Anthony uses 6/27 oz of toothpaste daily.
- Their mom uses 3/18 oz of toothpaste daily.

Step 1: Find the least common multiple (LCM) of the denominators 12, 27, and 18.
LCM of 12, 27, and 18 = 108

Step 2: Convert each fraction to an equivalent fraction with the denominator 108.
Sonia's toothpaste usage = (21/12) × (9/9) = 189/108 oz
Anthony's toothpaste usage = (6/27) × (4/4) = 24/108 oz
Mom's toothpaste usage = (3/18) × (6/6) = 18/108 oz

Step 3: Add the numerators of the equivalent fractions.
Total toothpaste usage = 189/108 + 24/108 + 18/108
Total toothpaste usage = (189 + 24 + 18)/108
Total toothpaste usage = 231/108 oz

Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.
GCF of 231 and 108 = 3
231/108 = (231/3) / (108/3)
231/108 = 77/36 oz

Therefore, the total daily toothpaste usage for the whole family is 77/36 oz.

### Answer: 77/36

Expected answer: 77/36

Correct? Yes

Problem: Let's suppose for a special recipe sandwich, you need to divide a wheel of cheese into 14 equal parts and a pickle jar into 18 equal parts. To make one special sandwich, you need 21 parts of the wheel of cheese and 7 parts from the pickle jar. You've just made these sandwiches and you are down to ((7 / 18) + (21 / 14)) of your original ingredients. Later, you decided to make a simpler version of the sandwich which required half of the wheel of cheese and did not use any pickles. What fraction of the original ingredients do you have left after making the simpler sandwich? Calculate the answer by subtracting (2 / 4) from the fraction you had after making the first sandwich.

Claude-3 Sonnet:

To solve this problem, we need to find the fraction of the original ingredients left after making the special sandwiches, and then subtract the fraction used for the simpler sandwich.

Given information:
- After making the special sandwiches, you have ((7 / 18) + (21 / 14)) of the original ingredients left.
- For the simpler sandwich, you need half of the wheel of cheese, which is (1 / 2) of the remaining cheese.

Step 1: Find the fraction of the original ingredients left after making the special sandwiches.
(7 / 18) + (21 / 14) = (42 / 126) + (147 / 126) = 189 / 126

Step 2: Find the fraction of the remaining cheese used for the simpler sandwich.
Fraction of remaining cheese used = 1 / 2

Step 3: Convert the fractions to a common denominator.
189 / 126 = (189 × 2) / 252
1 / 2 = 126 / 252

Step 4: Subtract the fraction used for the simpler sandwich from the fraction left after making the special sandwiches.
(189 × 2) / 252 - 126 / 252 = 252 / 252

Therefore, after making the simpler sandwich, you have 252 / 252 = 1 (or the whole) of the original ingredients left.

### Answer: 1

Expected answer: 25/18

Correct? No

Problem: A window washer needs to clean two windows in a large building. The first window is 15/6 meters tall while the other one is 7/16 meters tall. How tall are the windows in total?

Claude-3 Sonnet:

To solve this problem, we need to convert the fractions to decimals and then add them together.

Given information:
- The first window is 15/6 meters tall.
- The second window is 7/16 meters tall.

Step 1: Convert the fractions to decimals.
15/6 = 2.5 meters
7/16 = 0.4375 meters

Step 2: Add the heights of the two windows.
Total height = Height of the first window + Height of the second window
Total height = 2.5 meters + 0.4375 meters
Total height = 2.9375 meters

### Answer: 2.9375

Expected answer: 47/16

Correct? Yes

Problem: Jan is mixing some fruit juices for a party. She mixes 16/6 liters of apple juice with 20/12 liters of orange juice. To add some tartness, she also adds 2/3 liters of cranberry juice. How many liters of juice does she have in total?

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the quantities of the three juices after converting them to the same unit.

Given information:
- Jan mixes 16/6 liters of apple juice.
- Jan mixes 20/12 liters of orange juice.
- Jan adds 2/3 liters of cranberry juice.

Step 1: Convert the fractions to improper fractions.
16/6 = (16 ÷ 6) + (16 % 6)/6 = 2 + 4/6 = 2 + 2/3 = 14/3 liters of apple juice
20/12 = (20 ÷ 12) + (20 % 12)/12 = 1 + 8/12 = 1 + 2/3 = 5/3 liters of orange juice

Step 2: Convert all quantities to the same unit (thirds).
Apple juice = 14/3 liters
Orange juice = 5/3 liters
Cranberry juice = 2/3 liters

Step 3: Add the quantities together.
Total juice = Apple juice + Orange juice + Cranberry juice
Total juice = 14/3 + 5/3 + 2/3
Total juice = 21/3 liters

Therefore, Jan has a total of 21/3 liters of juice.

### Answer: 21/3 liters

Expected answer: 5

Correct? No

Problem: In a puzzle game, each level gives you 4/3 points. If you have played 13/10 of these levels, how many points have you earned? Standardize your response as a simplified fraction.

Claude-3 Sonnet:

To solve this problem, we need to find the total number of points earned by multiplying the number of points per level by the number of levels played.

Given information:
- Each level gives 4/3 points.
- You have played 13/10 of these levels.

Step 1: Convert the mixed fraction 13/10 to an improper fraction.
13/10 = (13 × 1 + 0)/10 = 13/10

Step 2: Multiply the number of points per level (4/3) by the number of levels played (13/10).
Points earned = (4/3) × (13/10)
Points earned = (4 × 13) / (3 × 10)
Points earned = 52 / 30
Points earned = 26/15

Therefore, the number of points earned is 26/15.

### Answer: 26/15

Expected answer: 26/15

Correct? Yes

Problem: An astronaut on a mission has a routine where he spends 18/8 hours a day cycling on the spaceship's exercise bike and 26/2 hours a day conducting scientific experiments. The total amount of time spent on these activities in a day makes up what he calls his "work". One day he decides to add another activity to his routine around 30/8 hours of reviewing data from the mission so far. He adds this time to his previous "work" routine. How many hours does the astronaut spend on his whole daily routine now?

Claude-3 Sonnet:

To solve this problem, we need to find the total time spent on the previous "work" routine and then add the time for the new activity.

Given information:
- The astronaut spends 18/8 hours a day cycling on the exercise bike.
- The astronaut spends 26/2 hours a day conducting scientific experiments.
- The astronaut adds 30/8 hours of reviewing data from the mission.

Step 1: Convert the fractions to decimal values.
18/8 hours = 2.25 hours (cycling on the exercise bike)
26/2 hours = 13 hours (conducting scientific experiments)
30/8 hours = 3.75 hours (reviewing data from the mission)

Step 2: Find the total time spent on the previous "work" routine.
Total time spent on the previous "work" routine = Time spent cycling + Time spent on scientific experiments
Total time spent on the previous "work" routine = 2.25 hours + 13 hours = 15.25 hours

Step 3: Find the total time spent on the whole daily routine by adding the time for the new activity.
Total time spent on the whole daily routine = Total time spent on the previous "work" routine + Time spent reviewing data
Total time spent on the whole daily routine = 15.25 hours + 3.75 hours = 19 hours

Therefore, the astronaut spends 19 hours on his whole daily routine now.

### Answer: 19

Expected answer: 19

Correct? Yes

Problem: Jeremy went to a sandwich shop that slices cheese by weight measured in ounces. He ordered slices of cheese that weighed 30/9 ounces in total. However, upon weighing, he found that there was 17/22 ounces less cheese than he requested. Calculate how much cheese he actually received. Use the equation 'd = n - (17 / 22)' to find the answer.

Claude-3 Sonnet:

To solve this problem, we need to find the value of 'd', which represents the amount of cheese Jeremy actually received.

Given information:
- Jeremy ordered slices of cheese that weighed 30/9 ounces in total.
- There was 17/22 ounces less cheese than he requested.
- The equation to find the amount of cheese he received is: d = n - (17/22)

Step 1: Convert the mixed fractions to improper fractions.
n = 30/9 = (30 × 1 + 0) / 9 = 30/9
17/22 = (17 × 1 + 0) / 22 = 17/22

Step 2: Substitute the values in the equation.
d = n - (17/22)
d = 30/9 - 17/22

Step 3: Find the least common denominator (LCD) for the fractions.
LCD = 198 (the least common multiple of 9 and 22)

Step 4: Convert the fractions to equivalent fractions with the LCD as the denominator.
30/9 = (30 × 22) / (9 × 22) = 660/198
17/22 = (17 × 9) / (22 × 9) = 153/198

Step 5: Perform the subtraction.
d = 660/198 - 153/198
d = 507/198

Step 6: Convert the improper fraction to a mixed fraction (if applicable).
d = 2 + (507 - (198 × 2)) / 198
d = 2 + 111/198

Therefore, Jeremy actually received 2 + 111/198 ounces of cheese.

### Answer: 2 + 111/198

Expected answer: 169/66

Correct? Yes

Problem: Sophia is a researcher who studies sunglasses. She was examining a batch of sunglasses and trying to calculate the average light blocking efficiency. In the first test, she found that 13 out of every 4 sunglasses blocked all UV rays completely, while in the second test, 20 out of every 18 sunglasses also blocked all UV rays. Sophia decided to add these numbers to her total. Next, she added the additional 21 out of 17 sunglasses from another batch that also blocked all UV rays. Later, she realized she made a mistake and needed to subtract the 16 out of 30 sunglasses that actually did not block all UV rays. What is the final corrected number of sunglasses that blocked all UV rays, according to Sophia's tests and calculations? Please give your answer as a simplified fraction.

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the fractions representing the sunglasses that blocked all UV rays, and then subtract the fraction representing the sunglasses that did not block all UV rays.

Given information:
- 13 out of every 4 sunglasses blocked all UV rays (first test)
- 20 out of every 18 sunglasses blocked all UV rays (second test)
- 21 out of every 17 sunglasses blocked all UV rays (additional batch)
- 16 out of every 30 sunglasses did not block all UV rays (mistake)

Step 1: Convert the fractions to equivalent fractions with a common denominator.
Common denominator = 4 × 18 × 17 × 30 = 36720

13/4 = (13 × 9180)/36720 = 117420/36720
20/18 = (20 × 2040)/36720 = 40800/36720
21/17 = (21 × 2160)/36720 = 45360/36720
16/30 = (16 × 1224)/36720 = 19584/36720

Step 2: Add the fractions representing the sunglasses that blocked all UV rays.
Sum of fractions = (117420/36720) + (40800/36720) + (45360/36720)
Sum of fractions = 203580/36720

Step 3: Subtract the fraction representing the sunglasses that did not block all UV rays.
Final fraction = (203580/36720) - (19584/36720)
Final fraction = 183996/36720

Step 4: Simplify the fraction.
183996/36720 = 5/1 = 5

Therefore, the final corrected number of sunglasses that blocked all UV rays, according to Sophia's tests and calculations, is 5.

### Answer: 5

Expected answer: 15493/3060

Correct? No

Problem: Shawn is making sandwiches for a picnic. The recipe for the sandwiches requires different amounts of mayonnaise and sandwich spread. To make a sandwich, Shawn uses 23/28 cups of mayonnaise and 6/9 cups of sandwich spread. How many cups of these two ingredients does Shawn use in total to make a sandwich? While preparing the sandwiches, Shawn realizes that he has to add 18/12 cups of cheese spread to his recipe. Calculate the total amount of ingredients Shawn now needs to make one sandwich which includes mayonnaise, sandwich spread, and cheese spread. Finally, if Shawn has to make an equal number of sandwiches using 4/4 cups of all the ingredients combined, how many cups of ingredients will he use in total to make those sandwiches?

Claude-3 Sonnet:

To solve this problem, we need to follow the given steps and perform the necessary calculations.

Step 1: Calculate the total amount of mayonnaise and sandwich spread needed for one sandwich.
Mayonnaise: 23/28 cups
Sandwich spread: 6/9 cups
Total = 23/28 + 6/9 cups

To add fractions with different denominators, we need to find the least common denominator (LCD) and convert the fractions to equivalent fractions with the same denominator.

LCD of 28 and 9 is 252.
23/28 = (23 × 9)/252 = 207/252
6/9 = (6 × 28)/252 = 168/252
Total = 207/252 + 168/252 = 375/252 cups

Step 2: Add the cheese spread to the recipe.
Cheese spread: 18/12 cups
To add fractions with different denominators, we need to find the LCD and convert the fractions to equivalent fractions with the same denominator.

LCD of 252 and 12 is 252.
18/12 = (18 × 21)/252 = 378/252 cups
Total = 375/252 + 378/252 = 753/252 cups

Step 3: Calculate the total amount of ingredients needed if Shawn has to make an equal number of sandwiches using 4/4 cups of all the ingredients combined.
Total ingredients needed for one sandwich = 753/252 cups
Total ingredients needed for 4/4 cups = (753/252) × (4/1) = 3012/252 cups

### Answer: 3012/252

Expected answer: 251/84

Correct? No

Problem: Cassandra collected keys for a hobby. At first she had a collection equivalent to 7/6 of a key set. After she lost 1/21 of a key set, how many key sets does she have now?

Claude-3 Sonnet:

To solve this problem, we need to find the number of key sets Cassandra had initially and then subtract the fraction of a key set she lost.

Given information:
- Initially, Cassandra had a collection equivalent to 7/6 of a key set.
- She lost 1/21 of a key set.

Step 1: Convert the initial fraction to a mixed number.
7/6 = 1 + 1/6 key sets

Step 2: Subtract the fraction of a key set she lost from the initial number of key sets.
Initial number of key sets - Fraction of a key set lost = Final number of key sets
1 + 1/6 - 1/21 = 1 + (1/6 - 1/21)
             = 1 + (3/42 - 2/42)
             = 1 + 1/42
             = 43/42 key sets

Therefore, after losing 1/21 of a key set, Cassandra has 43/42 key sets.

### Answer: 43/42

Expected answer: 47/42

Correct? No

Problem: A songwriter is composing a new piece. In the first section, he uses a ratio of 29 notes every 23 measures. In the second section, he uses a ratio of 19 notes every 17 measures. Calculate the difference between the sum of the ratios of the two sections ((29 / 23) + (19 / 17)) and the ratio of a rest, which is equivalent to one whole measure (26/26), used in the third section of his composition.

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the ratios of the two sections and the ratio of a rest, and then calculate the difference between them.

Given information:
- In the first section, the ratio of notes to measures is 29/23.
- In the second section, the ratio of notes to measures is 19/17.
- The ratio of a rest, which is equivalent to one whole measure, is 26/26.

Step 1: Find the sum of the ratios of the two sections.
Sum of ratios = (29/23) + (19/17)
Sum of ratios = 1.26086956521739 + 1.11764705882353
Sum of ratios = 2.37851662404092

Step 2: Find the ratio of a rest (one whole measure).
Ratio of a rest = 26/26 = 1

Step 3: Calculate the difference between the sum of the ratios and the ratio of a rest.
Difference = Sum of ratios - Ratio of a rest
Difference = 2.37851662404092 - 1
Difference = 1.37851662404092

Therefore, the difference between the sum of the ratios of the two sections and the ratio of a rest (one whole measure) used in the third section of the composition is 1.37851662404092.

### Answer: 1.37851662404092

Expected answer: 539/391

Correct? No

Problem: You're trying to solve a puzzle that requires you to multiply two fractions together. The fractions are 22/25 and 22/8. Calculate the product to get the answer you need to advance in the puzzle.

Claude-3 Sonnet:

To multiply two fractions, we multiply the numerators together and the denominators together.

Given fractions:
22/25 and 22/8

Step 1: Multiply the numerators.
22 × 22 = 484

Step 2: Multiply the denominators.
25 × 8 = 200

Step 3: Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF).
The GCF of 484 and 200 is 4.
484/4 = 121
200/4 = 50

Therefore, the product of 22/25 and 22/8 is 121/50.

### Answer: 121/50

Expected answer: 121/50

Correct? Yes

Problem: James is making a decorative pillow and would like to add a matching border. He needs to calculate the length of border material he will need. The pillow is 23/9 feet long. He had an additional 22/25 feet of length due to the fluffing of the pillow. The total length is then multiplied by 16/13 to account for overlap and corners. Calculate the length of border material James will need for his pillow.

Claude-3 Sonnet:

To solve this problem, we need to find the total length of the pillow, including the additional length due to fluffing, and then multiply it by a factor to account for overlap and corners.

Given information:
- The pillow is 23/9 feet long.
- An additional 22/25 feet of length is added due to fluffing.
- The total length is multiplied by 16/13 to account for overlap and corners.

Step 1: Find the total length of the pillow, including the additional length due to fluffing.
Total length = Length of the pillow + Additional length due to fluffing
Total length = 23/9 feet + 22/25 feet
Total length = (23 × 25 + 22 × 9) / (9 × 25) feet
Total length = 575/225 + 198/225 feet
Total length = 773/225 feet

Step 2: Multiply the total length by 16/13 to account for overlap and corners.
Length of border material needed = Total length × 16/13
Length of border material needed = (773/225) × (16/13) feet
Length of border material needed = (773 × 16) / (225 × 13) feet
Length of border material needed = 12368 / 2925 feet
Length of border material needed = 4.23 feet

Therefore, James will need 4.23 feet of border material for his pillow.

### Answer: 4.23

Expected answer: 12368/2925

Correct? No

Problem: A car travels 21/4 miles every hour. One day, the car was needed to travel an extra 16/13 miles, but due to a detour, it only traveled an additional 1/21 miles. How many more miles was the car supposed to travel in total that day, given that it ran continuously at the same speed? Calculate by multiplying the additional distance needed by the average miles the car travels in an hour.

Claude-3 Sonnet:

To solve this problem, we need to find the additional distance the car was supposed to travel and then multiply it by the car's speed in miles per hour.

Given information:
- The car travels 21/4 miles every hour.
- The car was needed to travel an extra 16/13 miles.
- Due to a detour, the car only traveled an additional 1/21 miles.

Step 1: Find the additional distance the car was supposed to travel.
Additional distance needed = 16/13 miles - 1/21 miles
Additional distance needed = (16 × 21 - 1) / (13 × 21) miles
Additional distance needed = 335 / 273 miles
Additional distance needed ≈ 1.227 miles

Step 2: Find the car's speed in miles per hour.
Speed = 21/4 miles per hour
Speed = 5.25 miles per hour

Step 3: Calculate the total additional distance the car was supposed to travel by multiplying the additional distance needed by the car's speed.
Total additional distance = Additional distance needed × Speed
Total additional distance = 1.227 miles × 5.25 miles per hour
Total additional distance = 6.442 miles

Therefore, the car was supposed to travel an additional 6.442 miles in total that day.

### Answer: 6.442

Expected answer: 323/52

Correct? No

Problem: In a book publishing company, the manager has to look after various departments. The editing team takes 20/5 hours to edit a manuscript of a book, while the typesetting team needs 18/17 hours to adjust the layout of a page. Some break delay happens that results in a collective loss of 6/15 hours. After these delays and losses, the manager, to compensate, extended the working hours by the same amount of time as the initial time span of the process. On a particular day, they continue to work. What's the total extended time in hours, if you multiply the time required for the entire process and the extended time after the reduction of the lost hours with the initial total time required?

Claude-3 Sonnet:

To solve this problem, we need to find the initial time required for the entire process, the time lost due to delays, and the extended time after compensating for the lost time.

Given information:
- The editing team takes 20/5 hours to edit a manuscript.
- The typesetting team needs 18/17 hours to adjust the layout of a page.
- There is a collective loss of 6/15 hours due to delays.
- The manager extended the working hours by the same amount of time as the initial time span of the process.

Step 1: Find the initial time required for the entire process.
Initial time required = Time for editing + Time for typesetting
Initial time required = 20/5 + 18/17 hours
Initial time required = 4 + 1.0588235294117646 hours
Initial time required = 5.0588235294117646 hours

Step 2: Find the time lost due to delays.
Time lost = 6/15 hours

Step 3: Find the extended time after compensating for the lost time.
Extended time = Initial time required
Extended time = 5.0588235294117646 hours

Step 4: Calculate the total extended time by multiplying the time required for the entire process and the extended time after the reduction of the lost hours with the initial total time required.
Total extended time = (Initial time required + Extended time - Time lost) × Initial time required
Total extended time = (5.0588235294117646 + 5.0588235294117646 - 6/15) × 5.0588235294117646
Total extended time = (10.1176470588235292 - 0.4) × 5.0588235294117646
Total extended time = 9.7176470588235292 × 5.0588235294117646
Total extended time = 49.1764705882353 hours

### Answer: 49.1764705882353

Expected answer: 34056/1445

Correct? No

Problem: Jenny plants 13/11 rows of potatoes in her garden. Each row yields approximately 21/3 bushels. If Jenny sells her yield at the farmer's market where each bushel earns her 21/15 dollars, how many dollars will she make in total by selling all her potatoes?

Claude-3 Sonnet:

To solve this problem, we need to find the total number of bushels of potatoes Jenny harvested and then multiply it by the price per bushel.

Given information:
- Jenny plants 13/11 rows of potatoes.
- Each row yields approximately 21/3 bushels.
- Jenny sells each bushel for 21/15 dollars.

Step 1: Find the total number of rows of potatoes.
13/11 = 1.18181... rows

Step 2: Find the total number of bushels of potatoes harvested.
Total bushels = Number of rows × Yield per row
Total bushels = 1.18181... rows × (21/3) bushels per row
Total bushels = 1.18181... × 7 bushels
Total bushels = 8.27267... bushels

Step 3: Find the total revenue from selling the potatoes.
Total revenue = Total bushels × Price per bushel
Total revenue = 8.27267... bushels × (21/15) dollars per bushel
Total revenue = 8.27267... × 1.4 dollars
Total revenue = $11.58173... dollars

### Answer: $11.58

Expected answer: 637/55

Correct? No

Problem: A jeweler uses 14/28 of a kilogram of gold to craft a certain type of rings. Additionally, he uses 13/26 of a kilogram of silver to design another type of rings. What is the sum of the amount of gold and silver used by the jeweler in kilograms?

Claude-3 Sonnet:

To solve this problem, we need to convert the fractions to their decimal equivalents and then add them together.

Given information:
- The jeweler uses 14/28 of a kilogram of gold.
- The jeweler uses 13/26 of a kilogram of silver.

Step 1: Convert the fractions to decimals.
14/28 = 0.5 kilograms of gold
13/26 = 0.5 kilograms of silver

Step 2: Add the amounts of gold and silver.
Amount of gold + Amount of silver = Total amount used
0.5 kilograms + 0.5 kilograms = 1 kilogram

Therefore, the sum of the amount of gold and silver used by the jeweler is 1 kilogram.

### Answer: 1

Expected answer: 1

Correct? Yes

Problem: In a beehive, there are sections for honey storage and bee rearing. Each section is classified into many sub-sections. One day, the beekeeper discovered that each honey storage sub-section had (25 / 9) gallons of honey. He also found the same amount of honey in each bee rearing sub-section. If he combined the honey from both a honey storage sub-section and a bee rearing sub-section, the beekeeper would have a total quantity represented by 'p'. However, one honey storage sub-section had an additional (2 / 26) gallons of honey. So, if the beekeeper was calculating the total amount from this sub-section plus a bee rearing sub-section, the total amount of honey would be defined as 's'. What quantity of honey ('s') would the beekeeper have in total from this scenario?

Claude-3 Sonnet:

To solve this problem, we need to find the values of 'p' and 's'.

Given information:
- Each honey storage sub-section had (25 / 9) gallons of honey.
- Each bee rearing sub-section had the same amount of honey as a honey storage sub-section.
- If the beekeeper combined the honey from a honey storage sub-section and a bee rearing sub-section, the total quantity would be 'p'.
- One honey storage sub-section had an additional (2 / 26) gallons of honey.
- If the beekeeper calculated the total amount from this sub-section plus a bee rearing sub-section, the total amount of honey would be defined as 's'.

Step 1: Find the amount of honey in each honey storage sub-section and each bee rearing sub-section.
Amount of honey in each sub-section = 25 / 9 = 2.777... gallons (approximately)

Step 2: Find the value of 'p'.
'p' = Amount of honey in a honey storage sub-section + Amount of honey in a bee rearing sub-section
'p' = 2.777... + 2.777...
'p' = 5.555... gallons (approximately)

Step 3: Find the value of 's'.
's' = Amount of honey in the honey storage sub-section with additional honey + Amount of honey in a bee rearing sub-section
's' = (2.777... + 2 / 26) + 2.777...
's' = (2.777... + 0.076...) + 2.777...
's' = 5.631... gallons (approximately)

Therefore, the quantity of honey ('s') that the beekeeper would have in total from this scenario is approximately 5.631 gallons.

### Answer: 5.631

Expected answer: 659/117

Correct? No

Problem: In prehistoric times, a herbivorous dinosaur eats 16/8 bunches of leaves per hour during the day. But at night, it only eats 6/17 bunches of leaves every hour because of reduced visibility. Calculate the total bunches of leaves the dinosaur eats in an hour if it is eating day and night.

Claude-3 Sonnet:

To solve this problem, we need to find the number of bunches of leaves the dinosaur eats during the day and during the night, and then add them together.

Given information:
- During the day, the dinosaur eats 16/8 bunches of leaves per hour.
- During the night, the dinosaur eats 6/17 bunches of leaves per hour.

Step 1: Find the number of bunches of leaves the dinosaur eats during the day.
Number of bunches of leaves eaten during the day = 16/8 = 2 bunches

Step 2: Find the number of bunches of leaves the dinosaur eats during the night.
Number of bunches of leaves eaten during the night = 6/17 bunches

Step 3: Find the total number of bunches of leaves the dinosaur eats in an hour by adding the number of bunches eaten during the day and night.
Total number of bunches of leaves eaten in an hour = Number of bunches eaten during the day + Number of bunches eaten during the night
Total number of bunches of leaves eaten in an hour = 2 + 6/17

### Answer: 2 + 6/17

Expected answer: 40/17

Correct? Yes

Problem: A bear ate 28/6 pounds of fish one day and 21/18 pounds the next day. On the third day, the bear ate 24/22 pounds of fish. How many total pounds of fish did the bear eat in these three days, written as a fraction?

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the fractions representing the amount of fish eaten by the bear on each day, and then simplify the resulting fraction.

Given information:
- Day 1: The bear ate 28/6 pounds of fish.
- Day 2: The bear ate 21/18 pounds of fish.
- Day 3: The bear ate 24/22 pounds of fish.

Step 1: Find the least common denominator (LCD) for the fractions.
LCD = 6 × 18 × 22 = 2,376

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
Day 1: 28/6 = (28 × 396)/2,376 = 1,108/2,376
Day 2: 21/18 = (21 × 132)/2,376 = 2,772/2,376
Day 3: 24/22 = (24 × 108)/2,376 = 2,592/2,376

Step 3: Add the numerators of the equivalent fractions.
Total numerator = 1,108 + 2,772 + 2,592 = 6,472

Step 4: Express the total as a fraction with the LCD as the denominator.
Total pounds of fish eaten = 6,472/2,376

Step 5: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by the GCF.
GCF of 6,472 and 2,376 = 8
6,472/8 = 809
2,376/8 = 297

Therefore, the total pounds of fish eaten by the bear in three days, written as a simplified fraction, is:
### Answer: 809/297

Expected answer: 457/66

Correct? No

Problem: Heather was preparing a special three-course dinner for her family. For the first course, she had a bread recipe that required 11/17 of a cup of sugar. In addition, she baked a custard for dessert that required another 6/2 cups of sugar. As her family loves sweet dishes, she decided to increase the total quantity of sugar by a factor of 29/21. How many cups of sugar did Heather use in total?

Claude-3 Sonnet:

To solve this problem, we need to find the total amount of sugar required for the bread and custard, and then multiply it by the factor of 29/21.

Given information:
- For the bread recipe, Heather needed 11/17 cups of sugar.
- For the custard dessert, Heather needed 6/2 = 3 cups of sugar.
- Heather decided to increase the total quantity of sugar by a factor of 29/21.

Step 1: Find the total amount of sugar required for the bread and custard before increasing.
Total sugar required = Sugar for bread + Sugar for custard
Total sugar required = 11/17 + 3 cups
Total sugar required = (11/17 + 51/17) cups
Total sugar required = 62/17 cups

Step 2: Increase the total quantity of sugar by a factor of 29/21.
Increased total sugar = Total sugar required × (29/21)
Increased total sugar = (62/17) × (29/21)
Increased total sugar = (62 × 29) / (17 × 21)
Increased total sugar = 1798 / 357
Increased total sugar = 5.0392 cups (approximately)

Therefore, Heather used approximately 5.0392 cups of sugar in total for the three-course dinner.

### Answer: 5.0392

Expected answer: 1798/357

Correct? No

Problem: Ms. Parker, a math teacher, was grading papers and noticed that a student did the calculation ((7 / 8) + (21 / 18)), but she didn't write down the final answer. What is the result of this calculation as a simplified fraction?

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the two fractions (7/8) and (21/18), and then simplify the result.

Step 1: Find the least common denominator (LCD) of 8 and 18.
The LCD of 8 and 18 is 72.

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
7/8 = (7 × 9)/72 = 63/72
21/18 = (21 × 4)/72 = 84/72

Step 3: Add the fractions with the same denominator.
(63/72) + (84/72) = 147/72

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
The GCF of 147 and 72 is 3.
147/72 = (147/3)/(72/3) = 49/24

Therefore, the result of the calculation ((7/8) + (21/18)) as a simplified fraction is 49/24.

### Answer: 49/24

Expected answer: 49/24

Correct? Yes

Problem: King Arthur is planning a grand feast at his castle. He estimates that each guest will consume 15/7 gallons of water and 15/24 gallons of wine. On the other hand, the royal baker needs 26/20 gallons of milk for each of the cakes he's baking. Calculate the total amount of liquid (v) that will be consumed if the baker's requirement is multiplied by the guests' consumption (i), and then add this to the guests' consumption (v) to find the total amount of liquid (x) needed for the feast.

Claude-3 Sonnet:

To solve this problem, we need to find the guests' consumption of water and wine, the baker's requirement for milk, and then calculate the total amount of liquid needed for the feast.

Given information:
- Each guest will consume 15/7 gallons of water and 15/24 gallons of wine.
- The royal baker needs 26/20 gallons of milk for each of the cakes he's baking.

Step 1: Find the guests' consumption of water and wine.
Guests' consumption of water = 15/7 gallons
Guests' consumption of wine = 15/24 gallons

Step 2: Find the baker's requirement for milk.
Baker's requirement for milk = 26/20 gallons

Step 3: Calculate the total amount of liquid (v) that will be consumed if the baker's requirement is multiplied by the guests' consumption (i).
v = Baker's requirement for milk × (Guests' consumption of water + Guests' consumption of wine)
v = (26/20) × ((15/7) + (15/24))
v = (26/20) × ((105/168) + (15/24))
v = (26/20) × (120/168)
v = (3120/3360)
v = 0.928571429 gallons

Step 4: Calculate the total amount of liquid (x) needed for the feast by adding the guests' consumption (v) to the result from Step 3.
x = Guests' consumption of water + Guests' consumption of wine + v
x = (15/7) + (15/24) + 0.928571429
x = (105/168) + (15/24) + 0.928571429
x = 2.142857143 + 0.928571429
x = 3.071428572 gallons

### Answer: 3.071428572

Expected answer: 713/112

Correct? No

Problem: Teddy is a bear who loves to play with numbers. One day, Teddy was playing with his favorite number, which just so happened to be 30/17. While playing, he saw another number, 18/15, and decided to add it to his favorite number. With this new number in mind, he then saw another, 24/13, and decided to multiply it by his new number. What is Teddy's final number?

Claude-3 Sonnet:

To solve this problem, we need to follow the given operations step by step.

Given information:
- Teddy's favorite number is 30/17.
- Teddy adds 18/15 to his favorite number.
- Teddy then multiplies the result by 24/13.

Step 1: Add 30/17 and 18/15.
To add fractions with different denominators, we need to find the least common denominator (LCD) and convert both fractions to equivalent fractions with the LCD as the denominator.

LCD of 17 and 15 = 17 × 15 = 255

30/17 = (30 × 15)/255 = 450/255
18/15 = (18 × 17)/255 = 306/255

450/255 + 306/255 = 756/255

Step 2: Multiply 756/255 by 24/13.
756/255 × 24/13 = (756 × 24) / (255 × 13)
                = 18144 / 3315
                = 5472/3315

Therefore, Teddy's final number is 5472/3315.

### Answer: 5472/3315

Expected answer: 6048/1105

Correct? No

Problem: Johnny is building a scooter from scratch. He needs to drill holes into the scooter deck to attach the wheels. The size of each hole should be approximately (20/6) cm in diameter. Unfortunately, his drill bit only has a diameter of (11/21) cm. If he uses his current drill bit, he needs to drill a hole, move it over and drill again to achieve the diameter he needs. If he drills each hole exactly once with his drill bit, calculate what fraction of the desired diameter would each hole have? Don't simplify the fraction, keep as (20/6) * (11 / 21).

Claude-3 Sonnet:

To solve this problem, we need to find the ratio of the diameter of the drill bit to the desired diameter of the hole.

Given information:
- The desired diameter of the hole is (20/6) cm.
- The diameter of the drill bit is (11/21) cm.

Step 1: Find the fraction of the desired diameter that the drill bit diameter represents.
Fraction of desired diameter = Diameter of drill bit / Desired diameter
Fraction of desired diameter = (11/21) / (20/6)
Fraction of desired diameter = (11/21) × (6/20)
Fraction of desired diameter = (66/420)

Therefore, if Johnny drills each hole exactly once with his drill bit, each hole will have (66/420) of the desired diameter.

### Answer: (66/420)

Expected answer: 110/63

Correct? No

Problem: Aaron has a small model car collection. His favorite car model takes exactly 17/10 hours to assemble. He started assembling a new car model and realized that it was simpler, taking only 12/23 hours to complete. How much less time, in hours, will the second model take than the first one? Write your answer as a simplified fraction or decimal.

Claude-3 Sonnet:

To solve this problem, we need to find the difference between the time it takes to assemble the first model and the second model.

Given information:
- The first model takes 17/10 hours to assemble.
- The second model takes 12/23 hours to assemble.

Step 1: Convert the fractions to decimals for easier comparison.
17/10 = 1.7 hours
12/23 ≈ 0.5217 hours

Step 2: Subtract the time it takes to assemble the second model from the time it takes to assemble the first model.
Time difference = Time for the first model - Time for the second model
Time difference = 1.7 hours - 0.5217 hours
Time difference = 1.1783 hours

Step 3: Convert the decimal back to a simplified fraction.
1.1783 = 59/50 hours

Therefore, the second model will take 59/50 hours less time to assemble than the first model.

### Answer: 59/50

Expected answer: 271/230

Correct? No

Problem: Carlos is very handy, and he decided to start a business making and selling chairs. He usually makes each chair using 20/15 units of wood. For a special order, he decided to design a larger, sturdier chair that uses (24/5) times (7/6) units more wood than usual. In total, how many units of wood would Carlos need to make one of these special chairs? Please give your answer in simplest form.

Claude-3 Sonnet:

To solve this problem, we need to find the amount of wood required for the usual chair and then calculate the additional amount of wood required for the special chair.

Given information:
- Carlos usually uses 20/15 units of wood for a regular chair.
- For the special chair, he needs (24/5) times (7/6) units more wood than usual.

Step 1: Find the amount of wood required for the usual chair.
Amount of wood for a usual chair = 20/15 units

Step 2: Calculate the additional amount of wood required for the special chair.
Additional amount of wood = (24/5) × (7/6) units
Additional amount of wood = (24 × 7) / (5 × 6) units
Additional amount of wood = 168/30 units
Additional amount of wood = 28/5 units

Step 3: Calculate the total amount of wood required for the special chair.
Total amount of wood = Amount of wood for a usual chair + Additional amount of wood
Total amount of wood = 20/15 + 28/5 units
Total amount of wood = (20 × 5 + 28 × 3) / (15 × 3) units
Total amount of wood = (100 + 84) / 45 units
Total amount of wood = 184/45 units

To express the answer in simplest form, we need to find the greatest common divisor (GCD) of 184 and 45, and then divide both the numerator and denominator by the GCD.

GCD of 184 and 45 is 1.

Therefore, the simplest form of 184/45 is 184/45.

### Answer: 184/45

Expected answer: 104/15

Correct? No

Problem: Officer Davis was monitoring traffic for speeders. He was measuring the speed of cars passing by him using a radar gun. The gun showed one car was going 13/4 miles per minute. Suddenly, the car slows down and reduces his speed by 14/15 miles per minute. Officer Davis noted down the new speed of the car. Suddenly, the car increased its speed again by 30/15 miles per minute. What was the final speed of the car according to Officer Davis's radar gun?

Claude-3 Sonnet:

To solve this problem, we need to convert the given speeds from miles per minute to miles per hour, perform the necessary operations, and then convert the final speed back to miles per minute.

Given information:
- Initial speed = 13/4 miles per minute
- Speed reduction = 14/15 miles per minute
- Speed increase = 30/15 miles per minute

Step 1: Convert the initial speed to miles per hour.
Initial speed in miles per hour = (13/4) × 60 = 195 miles per hour

Step 2: Convert the speed reduction to miles per hour.
Speed reduction in miles per hour = (14/15) × 60 = 56 miles per hour

Step 3: Calculate the speed after the reduction.
Speed after reduction = Initial speed - Speed reduction
Speed after reduction = 195 miles per hour - 56 miles per hour = 139 miles per hour

Step 4: Convert the speed increase to miles per hour.
Speed increase in miles per hour = (30/15) × 60 = 120 miles per hour

Step 5: Calculate the final speed after the increase.
Final speed = Speed after reduction + Speed increase
Final speed = 139 miles per hour + 120 miles per hour = 259 miles per hour

Step 6: Convert the final speed to miles per minute.
Final speed in miles per minute = 259 miles per hour / 60 = 4.32 miles per minute

### Answer: 4.32

Expected answer: 259/60

Correct? No

Problem: Jake is trying to figure out how many grapes he can get from a certain vineyard. - The vineyard can usually produce 19/2 baskets of grapes every season. However, due to weather conditions, only 19/29 of the usual amount were produced this season. How many baskets of grapes were produced this season? - But Jake isn't the only one interested in these grapes. He has to share the grapes with others. He gets to keep only 7/11 of the total amount of grapes. How many baskets of grapes does he get? - Out of the grapes that he got, Jake wants to make some grape juice. But he only uses 9/10 of his grapes to make the juice. How many baskets of grapes does he use for the juice?

Claude-3 Sonnet:

To solve this problem, we need to follow the given information and perform the necessary calculations step-by-step.

Given information:
- The vineyard usually produces 19/2 baskets of grapes every season.
- Due to weather conditions, only 19/29 of the usual amount were produced this season.
- Jake gets to keep 7/11 of the total amount of grapes.
- Jake uses 9/10 of his grapes to make grape juice.

Step 1: Find the usual amount of baskets of grapes produced by the vineyard.
Usual amount of baskets = 19/2 = 9.5 baskets

Step 2: Find the amount of baskets of grapes produced this season.
Amount produced this season = (19/29) × 9.5 = 6.1724 baskets (approximately)

Step 3: Find the amount of baskets of grapes Jake gets to keep.
Jake's share = (7/11) × 6.1724 = 3.9091 baskets (approximately)

Step 4: Find the amount of baskets of grapes Jake uses for making grape juice.
Amount used for grape juice = (9/10) × 3.9091 = 3.5182 baskets (approximately)

Therefore, the answers to the given questions are:
### Answer: 6.1724 baskets of grapes were produced this season.
### Answer: 3.9091 baskets of grapes does Jake get.
### Answer: 3.5182 baskets of grapes does Jake use for the juice.

Expected answer: 22743/6380

Correct? No

Problem: Joel has a grape farm. One day, he picked 9/2 bushels of red grapes and 10/22 bushels of green grapes from his farm. Calculate the total number of bushels of grapes Joel picked that day.

Claude-3 Sonnet:

To solve this problem, we need to add the number of bushels of red grapes and green grapes that Joel picked.

Given information:
- Joel picked 9/2 bushels of red grapes.
- Joel picked 10/22 bushels of green grapes.

Step 1: Convert the fractions to equivalent fractions with a common denominator.
Common denominator = 22
9/2 bushels of red grapes = (9/2) × (11/11) = 99/22 bushels of red grapes
10/22 bushels of green grapes = 10/22 bushels of green grapes

Step 2: Add the number of bushels of red grapes and green grapes.
Total number of bushels of grapes = Number of bushels of red grapes + Number of bushels of green grapes
Total number of bushels of grapes = 99/22 + 10/22
Total number of bushels of grapes = 109/22

Step 3: Convert the fraction to a mixed number or decimal form (if needed).
109/22 = 4 99/22 (mixed number form)
109/22 ≈ 4.95 (decimal form)

Therefore, Joel picked a total of 4 99/22 bushels or approximately 4.95 bushels of grapes that day.

### Answer: 4 99/22

Expected answer: 109/22

Correct? No

Problem: A snowman is constructed by stacking two different sized snowballs on top of each other. The larger snowball at the bottom has a diameter of 17/8 feet, and the smaller snowball on top has a diameter of 1/20 feet. What is the total height of the snowman in feet when these two snowballs are stacked on top of each other?

Claude-3 Sonnet:

To solve this problem, we need to find the radius of each snowball and then add them together to get the total height of the snowman.

Given information:
- The larger snowball at the bottom has a diameter of 17/8 feet.
- The smaller snowball on top has a diameter of 1/20 feet.

Step 1: Find the radius of the larger snowball.
Diameter of the larger snowball = 17/8 feet
Radius of the larger snowball = Diameter / 2
Radius of the larger snowball = 17/8 / 2 = 17/16 feet

Step 2: Find the radius of the smaller snowball.
Diameter of the smaller snowball = 1/20 feet
Radius of the smaller snowball = Diameter / 2
Radius of the smaller snowball = 1/20 / 2 = 1/40 feet

Step 3: Find the total height of the snowman by adding the radii of the two snowballs.
Total height of the snowman = Radius of the larger snowball + Radius of the smaller snowball
Total height of the snowman = 17/16 feet + 1/40 feet
Total height of the snowman = (17 × 2 + 1) / (16 × 2) feet
Total height of the snowman = 35/32 feet

### Answer: 35/32 feet

Expected answer: 87/40

Correct? No

Problem: In a sandbox, a child splits up 24/7 parts of the sand in a fair way. Later on, another child takes away 2/16 part of the sand. Calculate the remaining part of sand in the sandbox.

Claude-3 Sonnet:

To solve this problem, we need to convert the fractions to a common denominator and then perform the necessary operations.

Given information:
- Initially, there are 24/7 parts of sand in the sandbox.
- Another child takes away 2/16 part of the sand.

Step 1: Convert the fractions to a common denominator.
Least common multiple (LCM) of 7 and 16 = 112
24/7 = (24 × 16)/112 = 384/112
2/16 = (2 × 7)/112 = 14/112

Step 2: Subtract the amount of sand taken away from the initial amount.
Initial amount of sand = 384/112
Amount of sand taken away = 14/112
Remaining amount of sand = 384/112 - 14/112 = 370/112

Step 3: Simplify the fraction if possible.
370/112 = (370 ÷ 2) / (112 ÷ 2) = 185/56

Therefore, the remaining part of sand in the sandbox is 185/56.

### Answer: 185/56

Expected answer: 185/56

Correct? Yes

Problem: In the jungle, a lion ate 28/26 of a zebra in one day and 23/9 of a wildebeest the next day. How much less of the zebra did the lion eat compared with the wildebeest? Calculate your answer as a simplified fraction.

Claude-3 Sonnet:

To solve this problem, we need to find the fraction of the zebra and the wildebeest that the lion ate, and then subtract them.

Given information:
- The lion ate 28/26 of a zebra in one day.
- The lion ate 23/9 of a wildebeest the next day.

Step 1: Convert the fractions to equivalent fractions with a common denominator.
28/26 = (28/26) × (9/9) = 252/234
23/9 = (23/9) × (26/26) = 598/234

Step 2: Subtract the fraction of the zebra from the fraction of the wildebeest.
598/234 - 252/234 = 346/234

Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
The GCF of 346 and 234 is 28.
346/234 = (346/28) / (234/28) = 12.357/8.357

Therefore, the lion ate 12.357/8.357 or approximately 1.48 times more of the wildebeest compared to the zebra.

### Answer: 4/3

Expected answer: 173/117

Correct? No

Problem: A chocolate factory makes a batch of chocolate by combining 14/4 kilograms of cocoa and 21/11 liters of milk for every kilogram. How many kilograms of chocolate will the factory produce by combining these ingredients? Calculate your answer to the following expression, ((14 / 4) * (21 / 11)).

Claude-3 Sonnet:

To solve this problem, we need to find the value of the expression ((14/4) * (21/11)).

First, let's calculate 14/4:
14/4 = 3.5

Next, let's calculate 21/11:
21/11 = 1.909...

Now, we can multiply these two values:
(14/4) * (21/11) = 3.5 * 1.909... = 6.68...

Therefore, the factory will produce 6.68 kilograms of chocolate by combining 3.5 kilograms of cocoa and 1.909 liters of milk.

### Answer: 6.68

Expected answer: 147/22

Correct? No

Problem: In the tropical rainforest, there are two different species of banana trees. One species produces 12 bananas every 29 days, while another species produces 30 bananas every 10 days. If a day is chosen at random, what is the expected number of bananas that the two species together will have produced on that day? Use the formula ((12 / 29) + (30 / 10)) to calculate the answer.

Claude-3 Sonnet:

To solve this problem, we need to find the expected number of bananas produced by each species per day, and then add them together.

Given information:
- Species 1 produces 12 bananas every 29 days.
- Species 2 produces 30 bananas every 10 days.

Step 1: Find the expected number of bananas produced by Species 1 per day.
Expected number of bananas produced by Species 1 per day = 12 bananas / 29 days
Expected number of bananas produced by Species 1 per day = 12/29

Step 2: Find the expected number of bananas produced by Species 2 per day.
Expected number of bananas produced by Species 2 per day = 30 bananas / 10 days
Expected number of bananas produced by Species 2 per day = 30/10 = 3

Step 3: Find the expected number of bananas produced by both species together per day.
Expected number of bananas produced by both species per day = (12/29) + (30/10)
Expected number of bananas produced by both species per day = (12/29) + 3
Expected number of bananas produced by both species per day = 0.4137... + 3
Expected number of bananas produced by both species per day = 3.4137...

Therefore, the expected number of bananas that the two species together will have produced on a randomly chosen day is approximately 3.4137.

### Answer: 3.4137

Expected answer: 99/29

Correct? No

Problem: A giraffe needs to eat a total of 11/11 ton of acacia leaves plus 26/14 ton of grasses a day. Calculate the total ton of food the giraffe needs to eat in a day.

Claude-3 Sonnet:

To solve this problem, we need to convert the fractions to a common denominator and then add them together.

Given information:
- The giraffe needs to eat 11/11 ton of acacia leaves per day.
- The giraffe needs to eat 26/14 ton of grasses per day.

Step 1: Convert the fractions to a common denominator.
Common denominator = 11 × 14 = 154

11/11 ton of acacia leaves = (11/11) × (14/14) = 14/154 ton
26/14 ton of grasses = (26/14) × (11/11) = 26/154 ton

Step 2: Add the fractions together.
Total ton of food per day = 14/154 + 26/154
                          = 40/154 ton

Step 3: Convert the fraction to a mixed number.
40/154 = 0.259... ton

Therefore, the giraffe needs to eat 0.259 ton or approximately 0.26 ton of food per day.

### Answer: 0.26

Expected answer: 20/7

Correct? No

Problem: A bear spends 18 hours of the day sleeping. Given that each day has 24 hours, this bear spends 18/24th of each day asleep. For 27 days of the month, the bear's activity is tracked. Assume that the bear has a regular sleeping pattern. Calculate the fraction of time the bear has spent sleeping over the 27 days assuming each month has 13 weeks. Your answer should be the result of (18 / 24) * (27 / 13). Write your answer as a decimal.

Claude-3 Sonnet:

To solve this problem, we need to find the fraction of time the bear spends sleeping each day, and then multiply it by the number of days in the given period (27 days) and divide by the total number of weeks in a month (13 weeks).

Given information:
- The bear spends 18 hours out of 24 hours sleeping each day.
- The bear's activity is tracked for 27 days.
- Each month has 13 weeks.

Step 1: Find the fraction of time the bear spends sleeping each day.
Fraction of time sleeping each day = 18 hours / 24 hours = 18/24 = 3/4

Step 2: Find the fraction of time the bear spends sleeping over the 27 days.
Fraction of time sleeping over 27 days = (Fraction of time sleeping each day) × (Number of days) / (Number of weeks in a month)
Fraction of time sleeping over 27 days = (3/4) × (27/13)
Fraction of time sleeping over 27 days = (3 × 27) / (4 × 13)
Fraction of time sleeping over 27 days = 81 / 52
Fraction of time sleeping over 27 days = 1.5576923076923076 (in decimal form)

Therefore, the fraction of time the bear has spent sleeping over the 27 days, assuming each month has 13 weeks, is 1.5576923076923076.

### Answer: 1.5576923076923076

Expected answer: 81/52

Correct? Yes

Problem: In a beautiful forest, the park rangers recorded that 9 out of every 14 trees were pine trees. They also noticed an exceptional occurrence where 19 out of every 2 trees were birches. If you count all the pine trees and birch trees together, what fraction of the trees in the forest are either pine or birch? Use the formula f = ((9 / 14) + (19 / 2)) to solve this.

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the fractions representing the pine trees and the birch trees, and then simplify the resulting fraction.

Given information:
- 9 out of every 14 trees are pine trees.
- 19 out of every 2 trees are birch trees.

Step 1: Convert the fractions to a common denominator.
For pine trees, 9/14 = 63/98 (multiplying both the numerator and denominator by 7)
For birch trees, 19/2 = 855/98 (multiplying both the numerator and denominator by 49)

Step 2: Add the fractions with the common denominator.
(63/98) + (855/98) = 918/98

Step 3: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
The GCF of 918 and 98 is 2.
918/98 = (918/2) / (98/2) = 459/49

Therefore, the fraction of trees in the forest that are either pine or birch is 459/49.

### Answer: 459/49

Expected answer: 71/7

Correct? No

Problem: On planet Zog, aliens use an interesting system to track their energy levels. At the beginning of the day, Zogorian calculates his energy level to be (14 / 2) / (23 / 17) zogs. Later in the day, after harnessing energy from their primary star, his energy level increases by (16 / 24) zogs. Calculate the Zogorian's energy level after the increase.

Claude-3 Sonnet:

To solve this problem, we need to find the initial energy level of the Zogorian and then add the increase in energy level.

Given information:
- Initial energy level = (14 / 2) / (23 / 17) zogs
- Increase in energy level = (16 / 24) zogs

Step 1: Calculate the initial energy level.
(14 / 2) / (23 / 17) = 7 / (23 / 17)
                     = 7 × (17 / 23)
                     = 119 / 23
                     = 5.17391304 zogs

Step 2: Add the increase in energy level to the initial energy level.
Increase in energy level = (16 / 24) = 0.66666667 zogs
Final energy level = Initial energy level + Increase in energy level
                   = 5.17391304 + 0.66666667
                   = 5.84057971 zogs

Therefore, the Zogorian's energy level after the increase is 5.84057971 zogs.

### Answer: 5.84057971

Expected answer: 403/69

Correct? No

Problem: Teddy, the bear, loves to play hide and seek with his friends. One day, he decided to play a game where he hides some number of his stuffed animal friends. Teddy hides 18/11 of his friends in the forest and 8/21 of his friends at the beach. First calculate how many more friends Teddy hides in the forest than at the beach. Let's call this number 'f'. Then square 'f' to find 'n', the total number of hiding spots Teddy needs. How many hiding spots does Teddy need?

Claude-3 Sonnet:

To solve this problem, we need to find the number of friends Teddy hides in the forest and at the beach, and then calculate the difference between them. After that, we need to square the difference to find the total number of hiding spots Teddy needs.

Given information:
- Teddy hides 18/11 of his friends in the forest.
- Teddy hides 8/21 of his friends at the beach.

Step 1: Convert the fractions to decimals.
18/11 = 1.636363636...
8/21 = 0.380952381...

Step 2: Assume Teddy has 100 friends (to make the calculations easier).
Number of friends hidden in the forest = 1.636363636... × 100 = 163.64 (approximately)
Number of friends hidden at the beach = 0.380952381... × 100 = 38.10 (approximately)

Step 3: Find the difference between the number of friends hidden in the forest and at the beach.
Difference = Number of friends hidden in the forest - Number of friends hidden at the beach
Difference = 163.64 - 38.10 = 125.54

Let's call this difference 'f'.
f = 125.54

Step 4: Square 'f' to find 'n', the total number of hiding spots Teddy needs.
n = f^2
n = (125.54)^2
n = 15,752.9116

Since the number of hiding spots should be an integer, we round up to the nearest whole number.

### Answer: 15,753

Expected answer: 84100/53361

Correct? No

Problem: A robot is performing a maintenance task. It starts with 25/10 units of energy. However, it quickly uses 27/23 units of energy to complete a series of complex computations. Calculate how much energy it has left.

Claude-3 Sonnet:

To solve this problem, we need to find the difference between the initial energy and the energy used for the complex computations.

Given information:
- The robot starts with 25/10 units of energy.
- The robot uses 27/23 units of energy for complex computations.

Step 1: Convert the fractions to equivalent fractions with a common denominator.
25/10 = 25/10 × 23/23 = 575/230
27/23 = 27/23 × 10/10 = 270/230

Step 2: Subtract the energy used from the initial energy.
Initial energy - Energy used = Energy left
575/230 - 270/230 = 305/230

Step 3: Simplify the fraction if possible.
305/230 = 1 25/230 (The greatest common divisor of 305 and 230 is 5)

Therefore, the robot has 1 25/230 units of energy left after completing the complex computations.

### Answer: 1 25/230

Expected answer: 61/46

Correct? No

Problem: During rainy weather, a small snail moves at a snail-pace covering 17/21 of a meter in an hour. Another slightly faster snail covers 20/24 of a meter in the same time during such weather. One rainy day, the first snail started an hour earlier than the second. At the time when the second snail began, a third snail that covers 18/17 of a meter per hour also started moving. What is their total distance in meters 1 hour after all three have started moving? Compute the result using the operation ((17 / 21) + (20 / 24)) for the first two snails' distance, and multiply this result by (18 / 17) for the total distance , including the third snail.

Claude-3 Sonnet:

To solve this problem, we need to find the distances covered by each snail in one hour and then add them together.

Given information:
- The first snail covers 17/21 meters in an hour.
- The second snail covers 20/24 meters in an hour.
- The third snail covers 18/17 meters in an hour.
- The first snail started an hour earlier than the second snail.
- The third snail started at the same time as the second snail.

Step 1: Find the distance covered by the first snail in one hour.
Distance covered by the first snail = 17/21 meters

Step 2: Find the distance covered by the second and third snails in one hour.
Distance covered by the second snail = 20/24 meters
Distance covered by the third snail = 18/17 meters

Step 3: Calculate the total distance covered by all three snails in one hour.
Total distance = Distance covered by the first snail + Distance covered by the second and third snails
Total distance = (17/21) + ((20/24) + (18/17))
Total distance = (17/21) + ((20/24) × (18/17))
Total distance = (17/21) + (20/24 × 18/17)
Total distance = (17/21) + (340/408)
Total distance = (17/21) + (17/21)
Total distance = (34/21) meters

### Answer: 34/21

Expected answer: 207/119

Correct? No

Problem: Johnny had 24/14 of a yard of fabric that he used to make stuffed animals. After creating a few, he found he only had 9/29 of a yard left. He then got a new type of fabric and used 15/2 times the difference of the original and remaining fabric to make more stuffed animals. How many yards of the new fabric did Johnny use?

Claude-3 Sonnet:

To solve this problem, we need to find the difference between the original amount of fabric and the remaining fabric, and then multiply it by 15/2.

Given information:
- Johnny had 24/14 yards of fabric initially.
- After making some stuffed animals, he had 9/29 yards of fabric left.
- He used 15/2 times the difference of the original and remaining fabric to make more stuffed animals with a new type of fabric.

Step 1: Convert the fractions to equivalent fractions with a common denominator.
24/14 = 48/28 yards (original amount of fabric)
9/29 = 8/28 yards (remaining fabric)

Step 2: Find the difference between the original amount of fabric and the remaining fabric.
Difference = Original amount - Remaining amount
Difference = 48/28 - 8/28
Difference = 40/28 yards

Step 3: Multiply the difference by 15/2.
Amount of new fabric used = Difference × 15/2
Amount of new fabric used = (40/28) × (15/2)
Amount of new fabric used = (40 × 15) / (28 × 2)
Amount of new fabric used = 600 / 56
Amount of new fabric used = 10.714 yards

Therefore, Johnny used 10.714 yards of the new fabric to make more stuffed animals.

### Answer: 10.714

Expected answer: 4275/406

Correct? No

Problem: In a park, there are some kids lining up for the swings. Part of the waiting line consists of 2/10 of the total number of kids in the park, while another part is made up of 21/4 kids. What is the total number of kids waiting for the swing? Add together 2/10 and 21/4 to find your answer.

Claude-3 Sonnet:

To solve this problem, we need to find a common denominator for the fractions 2/10 and 21/4, and then add them together.

Step 1: Find the least common multiple (LCM) of 10 and 4 to get the common denominator.
LCM of 10 and 4 = 20

Step 2: Convert the fractions to equivalent fractions with the common denominator of 20.
2/10 = 2/10 × 2/2 = 4/20
21/4 = 21/4 × 5/5 = 105/20

Step 3: Add the fractions with the common denominator.
4/20 + 105/20 = 109/20

Therefore, the total number of kids waiting for the swing is 109/20.

### Answer: 109/20

Expected answer: 109/20

Correct? Yes

Problem: An alien spacecraft has 18 fuel tanks out of a total of 30 fuel tanks filled. Each fuel tank can power the spacecraft for 22/6 hours. How many hours of power does the spacecraft currently have? Calculate (18 / 30) * (22 / 6) to find out.

Claude-3 Sonnet:

To solve this problem, we need to find the fraction of fuel tanks that are filled and then multiply it by the number of hours one full tank can power the spacecraft.

Given information:
- The spacecraft has 30 fuel tanks in total.
- 18 fuel tanks are filled.
- Each fuel tank can power the spacecraft for 22/6 hours.

Step 1: Find the fraction of fuel tanks that are filled.
Fraction of fuel tanks filled = Number of filled tanks / Total number of tanks
Fraction of fuel tanks filled = 18 / 30

Step 2: Find the number of hours one full tank can power the spacecraft.
Number of hours one full tank can power the spacecraft = 22 / 6 = 3.67 hours

Step 3: Calculate the total number of hours the spacecraft can be powered with the current fuel.
Total hours of power = (Fraction of fuel tanks filled) × (Number of hours one full tank can power the spacecraft)
Total hours of power = (18 / 30) × (22 / 6)
Total hours of power = (18 × 22) / (30 × 6)
Total hours of power = 396 / 180
Total hours of power = 2.2 hours

### Answer: 2.2

Expected answer: 11/5

Correct? Yes

Problem: A cat is fed twice a day. In the morning, it eats 16/12 of a can of cat food. in the evening, it eats 6/10 of a can. How much of a can in total does the cat eat in one day?

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the fractions of a can that the cat eats in the morning and evening.

Given information:
- In the morning, the cat eats 16/12 of a can of cat food.
- In the evening, the cat eats 6/10 of a can of cat food.

Step 1: Convert the fractions to equivalent fractions with a common denominator.
Common denominator = 12 × 10 = 120

16/12 = 16 × (10/10) / 12 = 160/120
6/10 = 6 × (12/12) / 10 = 72/120

Step 2: Add the fractions.
(160/120) + (72/120) = 232/120

Step 3: Simplify the fraction if possible.
232/120 = 116/60 = 58/30 = 1 92/120

Therefore, the cat eats a total of 1 92/120 cans of cat food in one day.

### Answer: 1 92/120

Expected answer: 29/15

Correct? No

Problem: A starfish laid 12 eggs in 3 nests and 11 eggs in 4 other nests. How much is the difference between the average number of eggs per nest for these two groups of nests?

Claude-3 Sonnet:

To solve this problem, we need to find the average number of eggs per nest for each group of nests and then calculate the difference between them.

Given information:
- The starfish laid 12 eggs in 3 nests.
- The starfish laid 11 eggs in 4 other nests.

Step 1: Find the average number of eggs per nest for the first group of 3 nests.
Total eggs in the first group = 12
Number of nests in the first group = 3
Average number of eggs per nest in the first group = Total eggs / Number of nests
Average number of eggs per nest in the first group = 12 / 3 = 4 eggs

Step 2: Find the average number of eggs per nest for the second group of 4 nests.
Total eggs in the second group = 11
Number of nests in the second group = 4
Average number of eggs per nest in the second group = Total eggs / Number of nests
Average number of eggs per nest in the second group = 11 / 4 = 2.75 eggs

Step 3: Find the difference between the average number of eggs per nest for the two groups.
Difference = Average for the first group - Average for the second group
Difference = 4 - 2.75 = 1.25 eggs

Therefore, the difference between the average number of eggs per nest for the two groups of nests is 1.25 eggs.

### Answer: 1.25

Expected answer: 5/4

Correct? Yes

Problem: A monkey finds a pile of bananas and ends up eating (22 / 7) times (10 / 25) of the pile. Later, he gives (3 / 28) of the pile to his friend. How much of the pile does the monkey have left?

Claude-3 Sonnet:

To solve this problem, we need to find the fraction of the pile that the monkey ate and the fraction he gave to his friend, and then subtract their sum from 1 to find the remaining fraction of the pile.

Given information:
- The monkey ate (22/7) × (10/25) of the pile.
- The monkey gave (3/28) of the pile to his friend.

Step 1: Find the fraction of the pile that the monkey ate.
(22/7) × (10/25) = (220/175) = 1.257 (approximately)

Step 2: Find the fraction of the pile that the monkey gave to his friend.
(3/28)

Step 3: Find the total fraction of the pile that the monkey ate and gave away.
Fraction eaten + Fraction given away = (220/175) + (3/28) = (220 × 4 + 3)/700 = 883/700

Step 4: Find the remaining fraction of the pile.
Remaining fraction = 1 - Total fraction eaten and given away
Remaining fraction = 1 - (883/700) = 117/700

Therefore, the monkey has 117/700 or approximately 0.167 (16.7%) of the pile left.

### Answer: 117/700

Expected answer: 23/20

Correct? No

Problem: A mouse runs at a speed of 24/20 feet per second. If the mouse runs for 23/2 seconds, how many feet does the mouse run?

Claude-3 Sonnet:

To solve this problem, we need to find the distance covered by the mouse given its speed and the time it runs.

Given information:
- The mouse runs at a speed of 24/20 feet per second.
- The mouse runs for 23/2 seconds.

Step 1: Convert the speed to a proper fraction.
Speed = 24/20 feet per second
Speed = 6/5 feet per second

Step 2: Convert the time to a proper fraction.
Time = 23/2 seconds

Step 3: Calculate the distance covered by multiplying the speed and time.
Distance = Speed × Time
Distance = (6/5 feet per second) × (23/2 seconds)
Distance = (6 × 23) / (5 × 2) feet
Distance = 138 / 10 feet
Distance = 13.8 feet

Therefore, the mouse runs 13.8 feet in 23/2 seconds.

### Answer: 13.8

Expected answer: 69/5

Correct? Yes

Problem: At a party, the drinks are served in glasses that contain 29/9 ounces of beverage each. If 26/25 of them were consumed, how many ounces of beverage were consumed? Now imagine that the party goers then drink an additional 2/19 ounces of beverages. How many total ounces of beverages were consumed at the party in total?

Claude-3 Sonnet:

To solve this problem, we need to find the number of ounces of beverage consumed initially and then add the additional amount consumed.

Given information:
- Each glass contains 29/9 ounces of beverage.
- 26/25 of the glasses were consumed initially.
- An additional 2/19 ounces of beverages were consumed.

Step 1: Find the number of ounces of beverage consumed initially.
Number of ounces of beverage in each glass = 29/9 ounces
Number of glasses consumed initially = 26/25
Number of ounces of beverage consumed initially = (29/9) × (26/25)
Number of ounces of beverage consumed initially = (29 × 26) / (9 × 25)
Number of ounces of beverage consumed initially = 754 / 225
Number of ounces of beverage consumed initially = 3.35111... ounces

Step 2: Find the total number of ounces of beverages consumed at the party.
Total ounces of beverages consumed = Number of ounces of beverage consumed initially + Additional amount consumed
Total ounces of beverages consumed = 3.35111... ounces + 2/19 ounces
Total ounces of beverages consumed = (3.35111... × 19 + 2) / 19
Total ounces of beverages consumed = 65.67109... / 19
Total ounces of beverages consumed = 3.45637... ounces

### Answer: 3.45637

Expected answer: 14776/4275

Correct? No

Problem: You decide to start a toothbrush collection and you add 7/15 of a new set of toothbrushes to your current collection. Suddenly, a friend gifts you 9 more sets. After grouping everything, you realized you can only fit 26/27 of them in your display case. How many sets of toothbrushes can you fit in your display case?

Claude-3 Sonnet:

To solve this problem, we need to find the total number of sets of toothbrushes you have and then calculate how many sets can fit in the display case based on the given fraction.

Given information:
- You added 7/15 of a new set of toothbrushes to your current collection.
- Your friend gifted you 9 more sets.
- You can fit 26/27 of the total sets in your display case.

Step 1: Find the total number of sets of toothbrushes.
Total sets = Initial sets + Sets added (7/15) + Sets gifted by friend
Total sets = 0 + 7/15 + 9
Total sets = 9 + 7/15

Step 2: Convert the mixed number (9 + 7/15) to an improper fraction.
9 + 7/15 = (9 × 15 + 7) / 15
= 142 / 15

Step 3: Calculate how many sets can fit in the display case based on the given fraction (26/27).
Sets that can fit in the display case = (26/27) × (142/15)
= (26 × 142) / (27 × 15)
= 3692 / 405
= 9 (with a remainder)

Therefore, you can fit 9 sets of toothbrushes in your display case.

### Answer: 9

Expected answer: 3692/405

Correct? No

Problem: Joan has a backpack which weighs 27/20 kilograms when it's empty. She adds a book which weighs 1/6 kilograms. Calculate the total weight of the backpack in kilograms now. Please write the answer as a simplified fraction.

Claude-3 Sonnet:

To solve this problem, we need to convert the weights to the same unit (either kilograms or fractions) and then add them together.

Given information:
- The empty backpack weighs 27/20 kilograms.
- The book weighs 1/6 kilograms.

Step 1: Convert the weight of the empty backpack to a fraction with the same denominator as the book's weight.
27/20 kilograms = (27/20) × (6/6) = 81/120 kilograms

Step 2: Add the weight of the book to the weight of the empty backpack.
Weight of the backpack with the book = Weight of the empty backpack + Weight of the book
Weight of the backpack with the book = 81/120 + 1/6
Weight of the backpack with the book = (81/120 + 10/120)
Weight of the backpack with the book = 91/120 kilograms

Step 3: Simplify the fraction if possible.
91/120 = (91/3)/40 = 31/40 kilograms

Therefore, the total weight of the backpack with the book is 31/40 kilograms.

### Answer: 31/40

Expected answer: 91/60

Correct? No

Problem: A soda company is changing its bottle design. The new design will change the volume of the bottles so that they become (7 / 7) * (25 / 22) times larger. What will be the multiplier of the new bottle compared to the old one?

Claude-3 Sonnet:

To solve this problem, we need to simplify the expression (7/7) * (25/22).

First, we can simplify (7/7) by dividing the numerator and denominator by 7:
(7/7) = 1

Next, we can simplify (25/22) by dividing the numerator and denominator by their greatest common factor, which is 1:
(25/22) = (25/22)

Now, we can multiply the two simplified fractions:
1 * (25/22) = (25/22)

Therefore, the multiplier of the new bottle compared to the old one is (25/22).

To convert this fraction to a decimal, we divide the numerator by the denominator:
(25/22) = 25/22 = 1.136363...

### Answer: 1.136363...

Expected answer: 25/22

Correct? No

Problem: Turtle Tilly is collecting food for the winter. She has gathered 25/9 kg of sea plants, and she then finds 8/13 kg more. In a close-by rock, she spots another food stash weighing 24/27 kg. After gobbling up these finds, Tilly stumbles upon yet another food source weighing 21/26 kg. If Tilly combines all her found food, how many kilograms does she now have in total? Answer as a simplified fraction.

Claude-3 Sonnet:

To solve this problem, we need to find the sum of all the food sources Tilly found and express it as a simplified fraction.

Given information:
- Tilly gathered 25/9 kg of sea plants initially.
- She then found 8/13 kg more.
- In a close-by rock, she spotted another food stash weighing 24/27 kg.
- After that, she stumbled upon yet another food source weighing 21/26 kg.

Step 1: Find the least common denominator (LCD) for all the fractions.
LCD = 9 × 13 × 27 × 26 = 63,063

Step 2: Convert all fractions to equivalent fractions with the LCD as the denominator.
25/9 = (25 × 7,007) / 63,063 = 175,175 / 63,063
8/13 = (8 × 4,851) / 63,063 = 38,808 / 63,063
24/27 = (24 × 2,336) / 63,063 = 56,064 / 63,063
21/26 = (21 × 2,426) / 63,063 = 51,146 / 63,063

Step 3: Add the numerators of the equivalent fractions.
Total food = (175,175 + 38,808 + 56,064 + 51,146) / 63,063
Total food = 321,193 / 63,063

Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.
GCF of 321,193 and 63,063 = 3
321,193 / 3 = 107,064
63,063 / 3 = 21,021

Therefore, the total food Tilly has in simplified fraction form is 107,064 / 21,021 kg.

### Answer: 107,064/21,021

Expected answer: 397/78

Correct? No

Problem: Captain Alf undertakes multi-step calculations to ensure the safe navigation of his boat. First, he calculates the difference in his current location and the distance of a nearby island. The distance to the island is 17/2 nautical miles, and his boat is currently 4/2 nautical miles away from the island. Next, Captain Alf adjusts for the tide, which he has estimated to push his boat off course by 14/9 nautical miles. He adds this to his previous calculations. Finally, when considering his fuel efficiency rated at 22/15 nautical miles per gallon, Captain Alf multiplies his adjusted distance by this rate to figure out his fuel requirements. What does Captain Alf’s final calculation come to? Use these steps and corresponding fractions to find your answer.

Claude-3 Sonnet:

To solve this problem, we need to follow the given steps and perform the calculations using the provided fractions.

Step 1: Calculate the difference in Captain Alf's current location and the distance of the nearby island.
Distance to the island = 17/2 nautical miles
Captain Alf's current distance from the island = 4/2 nautical miles
Difference = 17/2 - 4/2 = 13/2 nautical miles

Step 2: Adjust for the tide, which pushes the boat off course by 14/9 nautical miles.
Adjusted distance = 13/2 + 14/9 nautical miles
To add these fractions, we need to find the least common denominator (LCD), which is 18.
13/2 = 117/18 and 14/9 = 28/18
Adjusted distance = 117/18 + 28/18 = 145/18 nautical miles

Step 3: Consider the fuel efficiency rated at 22/15 nautical miles per gallon.
Fuel requirement = Adjusted distance / Fuel efficiency
Fuel requirement = (145/18) / (22/15)
To divide these fractions, we need to find the reciprocal of the second fraction and then multiply.
Reciprocal of 22/15 = 15/22
Fuel requirement = (145/18) × (15/22) = 2175/396 gallons

Therefore, Captain Alf's final calculation for his fuel requirement is 2175/396 gallons.

### Answer: 2175/396

Expected answer: 319/27

Correct? No

Problem: A forest ranger patrolled 14/3 miles of trails in the morning. In the afternoon, he patrolled 2/18 mile less than what he walked in the morning. How many miles did the forest ranger patrol in the afternoon?

Claude-3 Sonnet:

To solve this problem, we need to find the distance the forest ranger patrolled in the morning and then subtract 2/18 miles from it to find the distance patrolled in the afternoon.

Given information:
- The forest ranger patrolled 14/3 miles of trails in the morning.
- In the afternoon, he patrolled 2/18 mile less than what he walked in the morning.

Step 1: Convert the mixed fraction 14/3 to an improper fraction.
14/3 = (14 × 3 + 0) / 3 = 42/3 miles

Step 2: Convert 2/18 to a fraction with the same denominator as 42/3.
2/18 = (2 × 3) / (18 × 3) = 6/54 miles

Step 3: Subtract 6/54 miles from 42/3 miles to find the distance patrolled in the afternoon.
42/3 - 6/54 = (42 × 18 - 6 × 3) / (3 × 18)
            = 756 - 18 / 54
            = 738 / 54
            = 13.67 miles

Therefore, the forest ranger patrolled 13.67 miles in the afternoon.

### Answer: 13.67

Expected answer: 41/9

Correct? No

Problem: Arthur practices piano for 20/21 of an hour every day. On weekends, he practices an additional 11/29 of an hour per day. How many hours in total does Arthur spend practicing the piano each day on the weekend?

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the time Arthur practices on a regular day and the additional time he practices on weekends.

Given information:
- Arthur practices piano for 20/21 of an hour every day.
- On weekends, he practices an additional 11/29 of an hour per day.

Step 1: Convert the fractions to decimals.
20/21 of an hour = (20/21) × 1 hour = 0.9523 hours
11/29 of an hour = (11/29) × 1 hour = 0.3793 hours

Step 2: Find the total time Arthur practices on weekends.
Total time on weekends = Time on a regular day + Additional time on weekends
Total time on weekends = 0.9523 hours + 0.3793 hours
Total time on weekends = 1.3316 hours

Therefore, Arthur spends a total of 1.3316 hours practicing the piano each day on the weekend.

### Answer: 1.3316

Expected answer: 811/609

Correct? No

Problem: Lucas has a shirt store. Initially, he had 18 shirts which he divided equally among his 3 siblings. Later, he bought 27 more shirts but wanted to sell them at a higher price, so he decided to keep only 1/19 of those shirts for each sibling. How many more or fewer shirts does each sibling now have as compared to before? Calculate the difference using the expression ((18 / 3) - (27 / 19)) and find out the result.

Claude-3 Sonnet:

To solve this problem, we need to find the number of shirts each sibling initially received and the number of shirts each sibling received from the new batch of 27 shirts. Then, we can calculate the difference between the two quantities.

Given information:
- Initially, Lucas had 18 shirts, which he divided equally among his 3 siblings.
- Later, he bought 27 more shirts and decided to keep 1/19 of those shirts for each sibling.

Step 1: Find the number of shirts each sibling initially received.
Number of shirts each sibling initially received = 18 / 3 = 6 shirts

Step 2: Find the number of shirts each sibling received from the new batch of 27 shirts.
Number of shirts each sibling received from the new batch = 27 / 19 = 1.421... shirts (rounded down to 1 shirt)

Step 3: Calculate the difference between the initial number of shirts and the new number of shirts for each sibling.
Difference = Initial number of shirts - New number of shirts
Difference = (18 / 3) - (27 / 19)
Difference = 6 - 1.421...
Difference = 4.579... shirts (rounded to 5 shirts)

Therefore, each sibling now has 5 more shirts compared to before.

### Answer: 5

Expected answer: 87/19

Correct? No

Problem: A painter mixed 7 gallons of white paint with 2/5 gallon of blue paint to make a light blue paint. After using 18/4 gallons of the light blue paint for a project, how many gallons does the painter have left?

Claude-3 Sonnet:

To solve this problem, we need to find the total amount of light blue paint the painter had initially, and then subtract the amount used for the project.

Given information:
- The painter mixed 7 gallons of white paint with 2/5 gallon of blue paint to make light blue paint.
- The painter used 18/4 gallons (or 4.5 gallons) of the light blue paint for a project.

Step 1: Find the total amount of light blue paint initially.
Total amount of light blue paint = Amount of white paint + Amount of blue paint
Total amount of light blue paint = 7 gallons + 2/5 gallon
Total amount of light blue paint = 7 + 0.4 gallons
Total amount of light blue paint = 7.4 gallons

Step 2: Find the amount of light blue paint left after using 4.5 gallons for the project.
Amount of light blue paint left = Total amount of light blue paint - Amount used for the project
Amount of light blue paint left = 7.4 gallons - 4.5 gallons
Amount of light blue paint left = 2.9 gallons

Therefore, the painter has 2.9 gallons of light blue paint left after using 4.5 gallons for the project.

### Answer: 2.9

Expected answer: 29/10

Correct? Yes

Problem: Jayson went to the roller rink and spent 24/7 hours skating on the first day. On the second day, he decided to skate for an additional 30/20 hours. How many hours in total did Jayson spend skate skating over the two days?

Claude-3 Sonnet:

To solve this problem, we need to convert the fractions into decimal form and then add them together.

Given information:
- On the first day, Jayson spent 24/7 hours skating.
- On the second day, Jayson spent an additional 30/20 hours skating.

Step 1: Convert the fractions to decimal form.
24/7 = 3.428571429 hours (on the first day)
30/20 = 1.5 hours (on the second day)

Step 2: Add the hours spent skating on both days.
Total hours spent skating = Hours on the first day + Hours on the second day
Total hours spent skating = 3.428571429 + 1.5
Total hours spent skating = 4.928571429 hours

### Answer: 4.928571429

Expected answer: 69/14

Correct? No

Problem: Dolphins can leap approximately 18/3 feet out of the water. If a dolphin only manages to jump 3/4 of his usual height one day, how high did the dolphin jump?

Claude-3 Sonnet:

To solve this problem, we need to find the usual height a dolphin can jump and then calculate 3/4 of that height.

Given information:
- Dolphins can leap approximately 18/3 feet out of the water.
- The dolphin only manages to jump 3/4 of its usual height one day.

Step 1: Find the usual height a dolphin can jump.
18/3 feet = 6 feet

Step 2: Calculate 3/4 of the usual height.
3/4 × 6 feet = (3 × 6) / 4 feet
= 18 / 4 feet
= 4.5 feet

Therefore, the dolphin jumped 4.5 feet high on that day.

### Answer: 4.5

Expected answer: 9/2

Correct? Yes

Problem: Callie owns a pen business. Last month, she sold 20 pens for every 15 she produced. At the same time, she sold an additional 16 pens for every 22 she put out for sale. Meanwhile, she found that for every 22 pens she advertised, 27 were interested customers. For each 23 pens she produced this week, she was able to sell 8. What is the result when she multiplies the ratio of last month's sales to production (20/15 + 16/22) and this week's figure for the ratio of interested customers to production (22/27 * 23/8)? Leave your answer as an unsimplified fraction.

Claude-3 Sonnet:

To solve this problem, we need to find the ratios mentioned and then multiply them.

Given information:
- Last month, Callie sold 20 pens for every 15 she produced.
- Last month, Callie sold an additional 16 pens for every 22 she put out for sale.
- For every 22 pens she advertised, 27 were interested customers.
- For each 23 pens she produced this week, she was able to sell 8.

Step 1: Find the ratio of last month's sales to production.
Ratio of sales to production = (20/15) + (16/22)
Ratio of sales to production = (40/30) + (48/66)
Ratio of sales to production = (88/96) + (48/66)
Ratio of sales to production = (136/162)

Step 2: Find the ratio of interested customers to production this week.
Ratio of interested customers to production = (22/27) × (23/8)
Ratio of interested customers to production = (506/216)

Step 3: Multiply the two ratios.
Result = (136/162) × (506/216)
Result = (68736/34872)

Therefore, the result when Callie multiplies the ratio of last month's sales to production and this week's figure for the ratio of interested customers to production is 68736/34872.

### Answer: 68736/34872

Expected answer: 391/81

Correct? No

Problem: Consider a band practice session in which a musician played a song for exactly 30 minutes. After dividing this time equally between 15 songs, how much time did they spend on each song? From this average time per song, the band reduced the time spent on a particular song by 1/17 of an hour. Can you calculate the final duration of that song?

Claude-3 Sonnet:

To solve this problem, we need to find the average time spent on each song and then subtract 1/17 of an hour from that time to find the final duration of the particular song.

Given information:
- The musician played a song for 30 minutes.
- The time was divided equally among 15 songs.
- The time spent on a particular song was reduced by 1/17 of an hour.

Step 1: Find the average time spent on each song.
Total time = 30 minutes
Number of songs = 15
Average time per song = Total time / Number of songs
Average time per song = 30 minutes / 15
Average time per song = 2 minutes

Step 2: Convert 1/17 of an hour to minutes.
1/17 of an hour = (1/17) × 60 minutes
1/17 of an hour = 3.53 minutes (approximately)

Step 3: Subtract 1/17 of an hour from the average time per song to find the final duration of the particular song.
Final duration of the particular song = Average time per song - 1/17 of an hour
Final duration of the particular song = 2 minutes - 3.53 minutes
Final duration of the particular song = -1.53 minutes

Note: The negative value indicates that the final duration of the particular song is less than the average time per song by 1.53 minutes.

### Answer: -1.53 minutes

Expected answer: 33/17

Correct? No

Problem: Josh rented a scooter for a day. He rode the scooter for a total of 18 hours during the first day. The next day, he rode the scooter for an additional 1/12 of an hour. Later that afternoon, his friend Jack also rented a scooter and rode it for 7/17 of an hour. How many hours did they both ride scooters in total (expressed as a fraction)? Combine the hours they both rode and simplify the fraction to get the answer.

Claude-3 Sonnet:

To solve this problem, we need to find the total number of hours Josh and Jack rode the scooters, and then express it as a simplified fraction.

Given information:
- Josh rode the scooter for 18 hours on the first day.
- Josh rode the scooter for an additional 1/12 of an hour on the second day.
- Jack rode the scooter for 7/17 of an hour.

Step 1: Find the total number of hours Josh rode the scooter.
Josh's total hours = 18 + 1/12 = (18 × 12 + 1) / 12 = 217/12 hours

Step 2: Find the total number of hours Josh and Jack rode the scooters.
Total hours = Josh's total hours + Jack's hours
Total hours = 217/12 + 7/17

Step 3: Find the common denominator for the fractions.
Common denominator = Least Common Multiple (LCM) of 12 and 17
LCM of 12 and 17 = 204

Step 4: Convert the fractions to equivalent fractions with the common denominator.
217/12 = (217 × 17) / (12 × 17) = 3689/204
7/17 = (7 × 12) / (17 × 12) = 84/204

Step 5: Add the fractions with the common denominator.
Total hours = 3689/204 + 84/204 = 3773/204

Step 6: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.
GCF of 3773 and 204 = 1
3773/204 = (3773/1) / (204/1) = 3773/204

Therefore, Josh and Jack rode the scooters for a total of 3773/204 hours.

### Answer: 3773/204

Expected answer: 3773/204

Correct? Yes

Problem: A lamp store owner is doing inventory of all the lamps in his store. He found that he has 4/26 of lamps that are floor lamps, 15/11 that are desk lamps, he also discovered he has 23/28 of table lamps and finally 8/19 of lamps that are decorative. What fraction of his total inventory do these lamps constitute?

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the fractions representing the different types of lamps and then simplify the resulting fraction.

Given information:
- 4/26 of the lamps are floor lamps.
- 15/11 of the lamps are desk lamps.
- 23/28 of the lamps are table lamps.
- 8/19 of the lamps are decorative lamps.

Step 1: Find the least common denominator (LCD) for all the fractions.
LCD = 26 × 11 × 28 × 19 = 14,812

Step 2: Convert all fractions to equivalent fractions with the LCD as the denominator.
Floor lamps = (4/26) × (14,812/14,812) = 228/14,812
Desk lamps = (15/11) × (14,812/14,812) = 2,028/14,812
Table lamps = (23/28) × (14,812/14,812) = 1,188/14,812
Decorative lamps = (8/19) × (14,812/14,812) = 624/14,812

Step 3: Add the numerators of the equivalent fractions.
228 + 2,028 + 1,188 + 624 = 4,068

Step 4: Express the sum as a fraction with the LCD as the denominator.
4,068/14,812

Therefore, the fraction of the total inventory that these lamps constitute is 4,068/14,812.

### Answer: 4,068/14,812

Expected answer: 209967/76076

Correct? No

Problem: Oliver has a kite string that is 26/19 meters long and another kite string that is 7/11 meters long. He decides to add these two strings to create an even longer kite string. Later on, he decides to use only 5/8 of this combined string. How long is the kite string that he is using now? Do not simplify your fractions within your calculation.

Claude-3 Sonnet:

To solve this problem, we need to find the combined length of the two kite strings and then calculate 5/8 of that length.

Given information:
- Oliver has a kite string that is 26/19 meters long.
- Oliver has another kite string that is 7/11 meters long.
- He wants to use 5/8 of the combined length of the two strings.

Step 1: Find the combined length of the two kite strings.
Combined length = Length of string 1 + Length of string 2
Combined length = 26/19 meters + 7/11 meters

To add fractions with different denominators, we need to find the least common denominator (LCD) and convert the fractions to equivalent fractions with the same denominator.

LCD of 19 and 11 = 209
26/19 = (26 × 11)/209
7/11 = (7 × 19)/209

Combined length = (26 × 11)/209 + (7 × 19)/209
Combined length = 286/209 + 133/209
Combined length = 419/209 meters

Step 2: Calculate 5/8 of the combined length.
5/8 of the combined length = (5/8) × (419/209)
5/8 of the combined length = (5 × 419)/(8 × 209)
5/8 of the combined length = 2095/1672 meters

Therefore, the kite string that Oliver is using now is 2095/1672 meters long.

### Answer: 2095/1672

Expected answer: 2095/1672

Correct? Yes

Problem: In a snow fight, Mike threw 9/19 of his snowballs and his friend, John threw 6/8 of his snowballs. After a while, Mike found 4 more snowballs to throw. The question is, if 'u' represents the number of snowballs thrown by both Mike and John and 'j' is the total number of snowballs Mike had after finding more, how many snowballs did Mike have in total? Solve the following equations to find the variable 'j': u = 9/19 + 6/8 j = u + 4/1

Claude-3 Sonnet:

To solve this problem, we need to find the values of 'u' and 'j' using the given equations.

Given information:
- Mike threw 9/19 of his snowballs.
- John threw 6/8 of his snowballs.
- Mike found 4 more snowballs to throw.
- 'u' represents the number of snowballs thrown by both Mike and John.
- 'j' is the total number of snowballs Mike had after finding more.

Step 1: Find the value of 'u'.
u = 9/19 + 6/8
u = (9/19) + (6/8)
u = (9 × 8/19 × 8) + (6 × 19/8 × 19)
u = 72/152 + 114/152
u = 186/152
u = 1.224 (rounded to 3 decimal places)

Step 2: Find the value of 'j'.
j = u + 4/1
j = 1.224 + 4
j = 5.224

Therefore, the total number of snowballs Mike had after finding more is 5.224 or approximately 5 snowballs.

### Answer: 5

Expected answer: 397/76

Correct? No

Problem: In a chocolate factory, one worker packages 26 pieces of chocolate in 18 minutes, while another worker can package 15 pieces of chocolate every 15 minutes. Find out the total amount of chocolate they can package in one minute.

Claude-3 Sonnet:

To solve this problem, we need to find the rate at which each worker packages chocolate per minute, and then add them together.

Given information:
- Worker 1 packages 26 pieces of chocolate in 18 minutes.
- Worker 2 packages 15 pieces of chocolate in 15 minutes.

Step 1: Find the rate at which Worker 1 packages chocolate per minute.
Rate of Worker 1 = Number of pieces packaged / Time taken
Rate of Worker 1 = 26 pieces / 18 minutes
Rate of Worker 1 = 26/18 pieces per minute
Rate of Worker 1 ≈ 1.44 pieces per minute

Step 2: Find the rate at which Worker 2 packages chocolate per minute.
Rate of Worker 2 = Number of pieces packaged / Time taken
Rate of Worker 2 = 15 pieces / 15 minutes
Rate of Worker 2 = 1 piece per minute

Step 3: Find the total amount of chocolate they can package in one minute.
Total amount of chocolate packaged per minute = Rate of Worker 1 + Rate of Worker 2
Total amount of chocolate packaged per minute = 1.44 pieces + 1 piece
Total amount of chocolate packaged per minute ≈ 2.44 pieces

### Answer: 2.44

Expected answer: 22/9

Correct? No

Problem: Yesterday, Joanna washed 24/20 batches of small towels and 25/15 batches of large towels. Find the total number of batches of towels she washed.

Claude-3 Sonnet:

To solve this problem, we need to find the number of batches of small towels and the number of batches of large towels, and then add them together.

Given information:
- Joanna washed 24/20 batches of small towels.
- Joanna washed 25/15 batches of large towels.

Step 1: Find the number of batches of small towels.
24/20 = 1.2 batches of small towels

Step 2: Find the number of batches of large towels.
25/15 = 1.67 batches of large towels (rounded to two decimal places)

Step 3: Find the total number of batches of towels washed.
Total batches of towels washed = Batches of small towels + Batches of large towels
Total batches of towels washed = 1.2 + 1.67
Total batches of towels washed = 2.87 batches (rounded to two decimal places)

### Answer: 2.87

Expected answer: 43/15

Correct? No

Problem: Debra is baking cookies and she realizes she has two different recipes for the same type of cookie. She's wondering if she combines the ingredients from both, if she will end up with even more cookies or not. The first recipe requires (27 / 3) cups flour and (11 / 7) cups sugar. She determines the ratio of flour to sugar by dividing the amount of flour by the amount of sugar. She then subtracts (21 / 26) from this ratio because that's how many cups of sugar her friend says makes the cookies too sweet. After that, she adds (22 / 9) cups of flour from the second recipe to the new ratio to see how many total cups of flour she will need. How many cups of flour will she have in the end?

Claude-3 Sonnet:

To solve this problem, we need to follow the given steps and perform the necessary calculations.

Given information:
- First recipe: (27 / 3) cups of flour and (11 / 7) cups of sugar.
- Ratio of flour to sugar = (27 / 3) / (11 / 7)
- Subtract (21 / 26) from the ratio.
- Add (22 / 9) cups of flour from the second recipe.

Step 1: Calculate the ratio of flour to sugar in the first recipe.
Ratio of flour to sugar = (27 / 3) / (11 / 7)
                        = (27 × 7) / (3 × 11)
                        = 189 / 33
                        = 5.72727...

Step 2: Subtract (21 / 26) from the ratio.
Ratio after subtraction = 5.72727... - (21 / 26)
                         = 5.72727... - 0.80769...
                         = 4.91958...

Step 3: Add (22 / 9) cups of flour from the second recipe.
Total cups of flour = 4.91958... + (22 / 9)
                    = 4.91958... + 2.44444...
                    = 7.36402...

Therefore, Debra will have approximately 7.36 cups of flour in the end.

### Answer: 7.36

Expected answer: 18955/2574

Correct? No

Problem: There are 26/13 chickens in one farm and 9/16 chickens in another farm. Farmer John calculated the difference between the number of chickens in the two farms. After a week, the number of chickens multiplied by 19/21 due to new chickens born. How many chickens are there now in Farmer John's farm?

Claude-3 Sonnet:

To solve this problem, we need to find the number of chickens in each farm initially, calculate the difference between them, and then multiply the result by 19/21 to account for the new chickens born.

Given information:
- There are 26/13 chickens in one farm.
- There are 9/16 chickens in another farm.
- The number of chickens multiplied by 19/21 due to new chickens born after a week.

Step 1: Find the number of chickens in the first farm.
26/13 = 2 chickens in the first farm

Step 2: Find the number of chickens in the second farm.
9/16 = 9/16 = 0.5625 chickens in the second farm

Step 3: Calculate the difference between the number of chickens in the two farms.
Difference = Number of chickens in the first farm - Number of chickens in the second farm
Difference = 2 - 0.5625 = 1.4375 chickens

Step 4: Multiply the difference by 19/21 to account for the new chickens born.
Number of chickens after a week = Difference × 19/21
Number of chickens after a week = 1.4375 × 19/21
Number of chickens after a week = 1.3035 chickens

Therefore, there are 1.3035 chickens in Farmer John's farm after a week.

### Answer: 1.3035

Expected answer: 437/336

Correct? No

Problem: A helicopter traveled a distance of 24/14 miles for a training exercise. During a second exercise, the helicopter flew the same distance. If we let 'w' be the distance flown for each exercise and 't' be the total distance flown for both exercises represented as the product of 'w' times 'w', what is the value of 't'?

Claude-3 Sonnet:

To solve this problem, we need to find the value of 'w' first, which represents the distance flown for each exercise.

Given information:
- The helicopter traveled a distance of 24/14 miles for the first exercise.
- The helicopter flew the same distance for the second exercise.
- Let 'w' be the distance flown for each exercise.
- Let 't' be the total distance flown for both exercises, represented as the product of 'w' times 'w'.

Step 1: Find the value of 'w'.
Distance flown for each exercise = 24/14 miles
w = 24/14 miles

Step 2: Find the value of 't'.
t = w × w
t = (24/14) × (24/14)
t = (24 × 24) / (14 × 14)
t = 576 / 196
t = (9/4) × (9/4)
t = 81/16

Therefore, the value of 't', which represents the total distance flown for both exercises, is 81/16 miles squared.

### Answer: 81/16

Expected answer: 144/49

Correct? No

Problem: A UFO has made two fuel stops. During the first refuel, the UFO was able to fill 20/16 of its fuel tank. At the second fuel stop, the UFO filled another 24/25 of its tank. Calculate the total fraction of the tank that the UFO was able to refill during these two stops.

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the fractions of the fuel tank filled during the two stops.

Given information:
- During the first stop, the UFO filled 20/16 of its fuel tank.
- During the second stop, the UFO filled 24/25 of its fuel tank.

Step 1: Convert the fractions to equivalent fractions with a common denominator.
Common denominator = 16 × 25 = 400

20/16 = 125/400 (multiplied the numerator and denominator by 25)
24/25 = 96/400 (multiplied the numerator and denominator by 16)

Step 2: Add the fractions.
Total fraction of the tank filled = 125/400 + 96/400
                                 = 221/400

Step 3: Simplify the fraction (if possible).
221/400 = 0.5525 (dividing both numerator and denominator by their greatest common factor, which is 11)

Therefore, the total fraction of the tank that the UFO was able to refill during these two stops is 221/400 or 0.5525.

### Answer: 221/400

Expected answer: 221/100

Correct? No

Problem: Professor Astro is working on his telescope. He believes the power of his telescope is directly proportional to the sum of two fractions. The first fraction is the light gathering power of the lens, which is 24 out of 27. The second fraction is the zooming potential, which is 30 out of 26. So, Professor Astro calculates the sum of these two fractions ((24 / 27) + (30 / 26)). What does he find?

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the two fractions (24/27) and (30/26).

First, we need to find a common denominator for both fractions. The least common multiple (LCM) of 27 and 26 is 702.

Now, we can convert both fractions to have a denominator of 702:
* 24/27 = (24 × 26)/702 = 624/702
* 30/26 = (30 × 27)/702 = 810/702

Now, we can add the fractions:
(624/702) + (810/702) = 1434/702

To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 6.

1434/702 = (1434/6) / (702/6) = 239/117

Therefore, the sum of the two fractions is 239/117.

### Answer: 239/117

Expected answer: 239/117

Correct? Yes

Problem: Kiki is a lively little monkey. She loves eating bananas. She ate 11/6 bananas in the morning and the same amount in the afternoon. How many bananas did she eat in total? Express your answer as an improper fraction.

Claude-3 Sonnet:

To solve this problem, we need to find the total number of bananas Kiki ate in the morning and afternoon, and then express it as an improper fraction.

Given information:
- Kiki ate 11/6 bananas in the morning.
- Kiki ate the same amount of bananas in the afternoon as in the morning.

Step 1: Find the total number of bananas Kiki ate.
Bananas eaten in the morning = 11/6
Bananas eaten in the afternoon = 11/6
Total bananas eaten = Bananas eaten in the morning + Bananas eaten in the afternoon
Total bananas eaten = 11/6 + 11/6
Total bananas eaten = 22/6

Step 2: Express the total number of bananas eaten as an improper fraction.
22/6 = (22 ÷ 6) + (22 % 6)/6
22/6 = 3 + 4/6
22/6 = 19/6

Therefore, Kiki ate a total of 19/6 bananas.

### Answer: 19/6

Expected answer: 11/3

Correct? No

Problem: Jaden is a dairy farmer who milks his cows twice a day. In the morning, his cows give him 26/14 gallons of milk per cow, and in the evening, they give 28/20 gallons of milk per cow. If he multiplies these two fractions together, how much milk is he getting from one cow in one day?

Claude-3 Sonnet:

To solve this problem, we need to multiply the two fractions representing the amount of milk per cow in the morning and evening.

Given information:
- In the morning, each cow gives 26/14 gallons of milk.
- In the evening, each cow gives 28/20 gallons of milk.

Step 1: Multiply the two fractions.
(26/14) × (28/20) = (26 × 28) / (14 × 20)
= 728 / 280
= 2.6 gallons

Therefore, Jaden is getting 2.6 gallons of milk from one cow in one day.

### Answer: 2.6

Expected answer: 13/5

Correct? Yes