Gemini-1.5 Pro on 4.MD.A.2-fraction
Common Core Standard 4.MD.A.2-fraction
This standard covers the following:
Use the four operations to solve word problems involving distances, Intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Problem: Steve started with 38 dollars and spent it evenly over 8 days. Then he received an extra 11 dollars. John started with 18 dollars but then he spent the same amount of money as Steve had. John found 25 dollars on the street. How much money does John have now?
Gemini-1.5 Pro:
Reasoning: Steve spent 38/8 = <<38/8=4.75>>4.75 dollars each day for 8 days. So, John also spent 4.75 dollars, leaving him with 18-4.75 = <<18-4.75=13.25>>13.25 dollars. After finding more money, John has 13.25+25 = <<13.25+25=38.25>>38.25 dollars. ### Answer: 38.25
Expected answer: 109/4
Correct? No
Problem: You have $45 in your wallet. You find a coin on the street worth $27/30. How much money do you have in total?
Gemini-1.5 Pro:
Reasoning: We need to add the value of the coin to the amount of money you already have. That means we need to calculate $45 + $27/30. Since $27/30 is less than $1, the total amount of money you have will be a little bit more than $45, but less than $46. ### Answer: $45 27/30
Expected answer: 459/10
Correct? Yes
Problem: After picking up the coin worth $27/30, you find another pile of coins. This pile of coins is worth $5/36. How much money do you have in total now?
Gemini-1.5 Pro:
Reasoning: You started with $45 and then found a coin worth $27/30, bringing your total to $45 27/30. Now, we need to add the value of the new pile of coins, $5/36, to this amount. Adding the fractions separately, we get 27/30 + 5/36. To add these fractions, we need a common denominator. The least common denominator for 30 and 36 is 180. Converting the fractions to have a denominator of 180, we get (27/30) * (6/6) = 162/180 and (5/36) * (5/5) = 25/180. Adding these fractions, we get 162/180 + 25/180 = 187/180. This is equivalent to 1 7/180 Adding this to the whole dollar amount, we get $45 + $1 7/180 ### Answer: $46 7/180
Expected answer: 8287/180
Correct? Yes
Problem: Instead of finding a coin worth $27/30, you actually found a coin worth $43/30 when you went to the currency exchange. Now, how much money do you have in total?
Gemini-1.5 Pro:
Reasoning: First we need to figure out how much money $43/30 represents. Since 30/30 equals 1, we know that $43/30 is more than one dollar because 43 is greater than 30. We can rewrite $43/30 as a mixed number: $1 13/30. Adding that to the initial $45 we get: $45 + $1 13/30 = $46 13/30 ### Answer: $46 13/30
Expected answer: 1393/30
Correct? Yes
Problem: John has $17 in his bank account. He finds a loose change on his desk that amounts to $8/37. How much money does he have in total?
Gemini-1.5 Pro:
Reasoning: We need to add the loose change to John's existing bank account. This means we need to calculate 17 + 8/37. We can express 17 as a fraction with 37 as the denominator: 629/37. Therefore, the total amount of money John has is 629/37 + 8/37 = 637/37. ### Answer: 637/37
Expected answer: 637/37
Correct? Yes
Problem: After totaling his money, John decides to save more by doing some extra tasks. He earns $22 per task. If he completes a number of tasks equal to the total money he currently has, how much money will he have then?
Gemini-1.5 Pro:
Reasoning: John completes 637/37 tasks, and he earns $22 per task. Therefore, he earns a total of (637/37) * $22 = $374 from the tasks. To find the total amount of money he has, we add his earnings to his existing money: $374 + $637/37 = $14265/37 ### Answer: $14265/37
Expected answer: 14014/37
Correct? No
Problem: John initially thought he had $17 in his bank account. However, he recently discovered that he actually had $7 instead. If he still has the same amount of loose change amounting to $8/37 on his desk, what is his new total amount of money?
Gemini-1.5 Pro:
Reasoning: We need to add the loose change to John's corrected bank account balance. This means we need to calculate 7 + 8/37. We can express 7 as a fraction with 37 as the denominator: 259/37 Therefore, the total amount of money John has is 259/37 + 8/37 = 267/37. ### Answer: 267/37
Expected answer: 267/37
Correct? Yes
Problem: Sally wants to measure the distance of her bike route. Initially, she hesitates and travels only 47/50 of a mile. Then, she gains confidence and rides another 31 miles. Every day for the next 28 days, she completes the same distance. One day, she decided to detour and added an extra 32/24 miles to her regular bike route. How many miles in total did she travel after adding the extra traveling distance?
Gemini-1.5 Pro:
Reasoning: First find the total distance of her regular bike route: 47/50 + 31 = <<47/50+31=31.94>>31.94 miles. Then multiply that distance by the number of days she rode her bike to find the total distance she traveled on those days: 31.94 x 28 = <<31.94*28=894.32>> 894.32 miles. Then add the distance of her detour to find her total distance traveled after the detour: 894.32 + 32/24 = <<894.32+32/24=895.65>>895.65 miles ### Answer: 895.65 miles
Expected answer: 67174/75
Correct? No
Problem: A train travels at a steady speed of 47 miles per hour for 4 hours. How far does the train travel in that time?
Gemini-1.5 Pro:
Reasoning: The train travels 47*4 = <<47*4=188>>188 miles in 4 hours. ### Answer: 188 miles
Expected answer: 188
Correct? Yes
Problem: If instead of traveling for 4 hours initially, the train had traveled for 18 hours at the same speed of 47 miles per hour, how far would the train have traveled in that time?
Gemini-1.5 Pro:
Reasoning: The train would travel 47*18 = <<47*18=846>>846 miles in 18 hours. ### Answer: 846 miles
Expected answer: 846
Correct? Yes
Problem: A truck can travel a distance of 34/25 kilometers on a liter of fuel. If 11 more kilometers are added to its journey, what is the total distance the truck can travel before running out of fuel? Then, if an additional 49 kilometers are added to the journey, what would be the total distance then?
Gemini-1.5 Pro:
Reasoning: First find the initial distance the truck can travel: 34/25 kilometers. Then add the additional 11 kilometers to find the total distance for the first part of the problem: (34/25) + 11 = 309/25 kilometers. Then add the final 49 kilometers to the first total distance calculated: (309/25) + 49 = 1534/25 kilometers ### Answer: 1534/25 kilometers
Expected answer: 1534/25
Correct? Yes
Problem: Instead of the previous scenario, now consider that the truck can travel a distance of 30 kilometers more than the distance it can cover on one liter of fuel which is 34/25 kilometers. If an additional 49 kilometers are then added to the journey, what would be the total distance then?
Gemini-1.5 Pro:
Reasoning: The truck can initially travel 30 kilometers more than 34/25 kilometers, totaling (34/25) + 30 = 784/25 kilometers. Adding the additional 49 kilometers, the final total distance becomes (784/25) + 49 = 2009/25 kilometers. ### Answer: 2009/25 kilometers
Expected answer: 2009/25
Correct? Yes
Problem: John drank a special energy drink that increased his jogging speed. After the energy drink, he was able to jog 50/49 miles per hour faster. One day, he had a speed of 4/22 miles per hour without the use of the energy drink. After consuming the energy drink, at what rate would he jog if he continued for 46/30 hours?
Gemini-1.5 Pro:
Reasoning: First, find John's increased speed: 50/49 + 4/22 = 1298/1078 miles per hour. Let's simplify 1298/1078 by dividing by the greatest common factor of 1298 and 1078 (which is 2): 1298/2 = 649 and 1078/2 = 539, so his increased speed is 649/539 miles per hour. To find the distance he covers in 46/30 hours, we multiply his increased speed by the time: (649/539) * (46/30) = 30054/16170 miles. Now, let's simplify 30054/16170 by dividing by the greatest common factor of 30054 and 16170 (which is 6): 30054/6 = 5009 and 16170/6 = 2695, so the simplified distance is 5009/2695 miles. ### Answer: 5009/2695 miles
Expected answer: 4968/2695
Correct? No
Problem: A truck driver starts his route with 9 gallons of gas in his tank. He stops at a station and adds to this tank another 21/36 gallons of gas. Later, he stops at another station and adds another 26/42 gallons of gas. How many gallons of gas total does the truck driver have now in his tank?
Gemini-1.5 Pro:
Reasoning: We need to add the amount of gas in the tank at the start to the amount added at each stop: 9 + 21/36 + 26/42. First, we need to simplify our fractions. Both 21 and 36 share a common factor of 3: 21/3 = 7, and 36/3 = 12, so 21/36 simplifies to 7/12. Both 26 and 42 share a common factor of 2: 26/2=13, and 42/2 = 21, so 26/42 simplifies to 13/21. Now our problem is: 9 + 7/12 + 13/21. To add these numbers, we need to convert our fractions to a common denominator. The least common denominator for our fractions is 84. 7/12 is equivalent to 49/84 (because 7 * 7 = 49, and 12 * 7 = 84). 13/21 is equivalent to 52/84 (because 13 * 4 = 52, and 21 * 4 = 84). 9 is equivalent to 756/84 (because 9 * 84 = 756). Now our problem is: 756/84 + 49/84 + 52/84. This is equal to 857/84, or 10 17/84. ### Answer: 10 17/84 gallons
Expected answer: 857/84
Correct? Yes
Problem: In the previous problem the truck driver has just reached his final total of gasoline in his tank. Now, suppose that his truck uses up this fuel at a rate by which each gallon lasts for 35 miles. How far can he continue to drive with the total amount of gasoline he has in his tank?
Gemini-1.5 Pro:
Reasoning: We know from the previous problem that the truck driver has 10 17/84 gallons of gas in his tank. To find out how many miles he can drive, we need to multiply this amount by the number of miles per gallon: 10 17/84 * 35. First, we need to convert our fraction into a decimal. 17/84 equals 0.2023 (rounded to the nearest ten thousandth). Now, our problem is: 10.2023 * 35. 10.2023 * 35 = 357.0805. ### Answer: 357.0805 miles
Expected answer: 4285/12
Correct? No
Problem: In the previous problem, we calculated how much fuel the truck driver had after adding 21/36 gallons and 26/42 gallons to 9 original gallons. Suppose now we mistakenly thought that the second stop was dispensing fuel faster and he actually added 26/4 gallons instead of 26/42 gallons in the second stop. If he still had the original 9 gallons to start with and added the 21/36 gallons in the first stop as per the original scenario, how much fuel would the truck driver have now in his truck after making both stops?
Gemini-1.5 Pro:
Reasoning: We can solve this by following a similar process as the original problem: 9 + 21/36 + 26/4. We already know 21/36 simplifies to 7/12. We can simplify 26/4 to 13/2 (because 26/2 = 13 and 4/2 = 2). Now our problem is 9 + 7/12 + 13/2. To add these, we need to convert to a common denominator. The least common denominator for our fractions is 12. 13/2 is equivalent to 78/12 (because 13 * 6 = 78 and 2 * 6 = 12). 9 is equivalent to 108/12 (because 9 * 12 = 108). Now our problem is 108/12 + 7/12 + 78/12. This is equal to 193/12, or 16 1/12. ### Answer: 16 1/12 gallons
Expected answer: 193/12
Correct? Yes
Problem: John has 6 dollars in his pocket. He then earns an additional 47/8 dollars from mowing his neighbor's lawn. How much money does he now have in total?
Gemini-1.5 Pro:
Reasoning: We need to add the amount John earned to his existing amount: 6 + 47/8. To do this, we can express 6 as a fraction with a denominator of 8: 6 = 48/8. Now, we can add the fractions: 48/8 + 47/8 = 95/8. ### Answer: 95/8 dollars
Expected answer: 95/8
Correct? Yes
Problem: John has 6 dollars in his pocket. He then earns an additional 47/8 dollars from mowing his neighbor's lawn. After that, his dad gives him an extra 41/10 dollars for cleaning the house. How much money does John now have in total?
Gemini-1.5 Pro:
Reasoning: First find the total John has after mowing the lawn: 6 + 47/8. We can write 6 as 48/8, so 48/8 + 47/8 = 95/8 dollars. Then add the amount his dad gave him: 95/8 + 41/10. To add these fractions, we need a common denominator, which is 40. So, 95/8 is equivalent to 475/40, and 41/10 is equivalent to 164/40. Finally, 475/40 + 164/40 = 639/40 dollars. ### Answer: 639/40 dollars
Expected answer: 639/40
Correct? Yes
Problem: In the previous problem, John originally had 6 dollars in his pocket. But what if he initially had 33 dollars instead? If he then earns an additional 47/8 dollars from mowing his neighbor's lawn, how much money would he have now?
Gemini-1.5 Pro:
Reasoning: Similar to the previous problem, we need to add the amount John earned to his initial amount: 33 + 47/8. Let's express 33 as a fraction with a denominator of 8: 33 = 264/8. Now we can add: 264/8 + 47/8 = 311/8. ### Answer: 311/8 dollars
Expected answer: 311/8
Correct? Yes
Problem: Matthew has $29 saved up. He buys a toy robot for $5. After buying the toy, he receives $8 from his grandmother for his birthday. How much money does Matthew have now?
Gemini-1.5 Pro:
Reasoning: After buying the toy robot, Matthew has $29 - $5 = <<29-5=24>>24 left. After his grandmother gives him money, Matthew has $24 + $8 = <<24+8=32>>32. ### Answer: $32
Expected answer: 32
Correct? Yes
Problem: A barrel of oil costs $16 and a refinery buys 9 barrels. How much do 9 barrels of oil cost in total?
Gemini-1.5 Pro:
Reasoning: Each barrel costs $16, so 9 barrels cost 9 * $16 = $<<9*16=144>>144. ### Answer: $144
Expected answer: 144
Correct? Yes
Problem: If the cost of a barrel of oil increases to $30, how much would it now cost for the refinery to buy the same 9 barrels of oil?
Gemini-1.5 Pro:
Reasoning: With the increased price, 9 barrels would now cost 9 * $30 = $<<9*30=270>>270. ### Answer: $270
Expected answer: 270
Correct? Yes
Problem: Amy's garden is 11 feet long. She plans to expand it by 30 more feet. At the end of this expansion, she decided to further extend the garden by the length equivalent to 30 divided by 13 feet. What will be the total length of her garden after all the expansions?
Gemini-1.5 Pro:
Reasoning: First expansion: 11 feet + 30 feet = 41 feet. Second expansion: 30 feet / 13 = 2.31 feet (approximately). Total Length = 41 feet + 2.31 feet = 43.31 feet (approximately). ### Answer: 43.31 feet (approximately)
Expected answer: 563/13
Correct? No
Problem: John's house is (17 / 3) miles from his work. The supermarket is (25 / 41) miles closer to his work than his house. How far is the supermarket from his work?
Gemini-1.5 Pro:
Reasoning: To find out how far the supermarket is from work, we need to subtract the distance the supermarket is closer to his work from the distance between John's house and work. This means we need to calculate (17/3) - (25/41). To subtract fractions, they need a common denominator. The least common denominator for 3 and 41 (since they are both prime numbers) is their product: 3 * 41 = 123. Let's convert each fraction to have the denominator 123: * (17/3) * (41/41) = 697/123 * (25/41) * (3/3) = 75/123 Now we can subtract: (697/123) - (75/123) = 622/123 ### Answer: 622/123 miles
Expected answer: 622/123
Correct? Yes
Problem: John wants to know the square of the distance between his work and the supermarket. Calculate this square distance.
Gemini-1.5 Pro:
Reasoning: We know from the previous problem that the supermarket is (622/123) miles from John's work. To find the square of this distance, we simply multiply the fraction by itself: (622/123) * (622/123) = 386884 / 15129 ### Answer: 386884/15129 square miles
Expected answer: 386884/15129
Correct? Yes
Problem: Suppose the supermarket was actually (25 / 46) miles closer to his work than his house instead of the previous distance. How far is the supermarket from his work in this case?
Gemini-1.5 Pro:
Reasoning: Similar to the previous problem, we need to subtract the new distance the supermarket is closer to his work from the distance between John's house and work. Again, John's house is (17/3) miles from work. We need to calculate (17/3) - (25/46). The least common denominator for 3 and 46 is their product: 3 * 46 = 138 Convert each fraction to have the denominator 138: * (17/3) * (46/46) = 782/138 * (25/46) * (3/3) = 75/138 Now we can subtract: (782/138) - (75/138) = 707/138 ### Answer: 707/138 miles
Expected answer: 707/138
Correct? Yes
Problem: A bank has $12 in one-dollar bills. They received an additional $36 from a deposit. After paying out $8, how much money does the bank now have in one-dollar bills?
Gemini-1.5 Pro:
Reasoning: The bank had a total of $12 + $36 = <<12+36=48>>$48 before the payout. After paying out $8, the bank has $48 - $8 = <<48-8=40>>$40 left. ### Answer: $40
Expected answer: 40
Correct? Yes
Problem: Following the previous scenario, suppose the bank received an uncommon payment of $19/11. How much money does the bank have now in one-dollar bills after this unusual deposit?
Gemini-1.5 Pro:
Reasoning: We need to figure out how many whole dollars are in $19/11. Since 19 divided by 11 is 1 with a remainder, there is $1 in one-dollar bills. Adding that to the bank's current amount gives us $40 + $1 = <<40+1=41>>$41 ### Answer: $41
Expected answer: 459/11
Correct? No
Problem: Following the previous scenario, suppose the bank had originally started with $12 in one-dollar bills. But this time, they received a smaller deposit of $22 instead of $36. After paying out the same $8, how much would the bank now have in one-dollar bills in this revised situation?
Gemini-1.5 Pro:
Reasoning: The bank had a total of $12 + $22 = <<12+22=34>>$34 after the smaller deposit. After paying out $8, the bank has $34 - $8 = <<34-8=26>>$26 left. ### Answer: $26
Expected answer: 26
Correct? Yes
Problem: Samantha has $28 in her bank account. Later, she found a few coins amounting to 46/41 dollars on the street and added them to her savings. How much money does she have now in her bank account?
Gemini-1.5 Pro:
Reasoning: 46/41 dollars is equal to $1.12. Samantha now has 28 + 1.12 = $29.12 in her bank account. ### Answer: $29.12
Expected answer: 1194/41
Correct? No
Problem: In a money counting contest, James had $37. Then his little brother gave him 14/19 of a dollar from his piggy bank. How much money does James have now?
Gemini-1.5 Pro:
Reasoning: James' little brother gave him 14/19 * $1.00 = $0.74 (rounded to the nearest cent). James now has $37 + $0.74 = $37.74. ### Answer: $37.74
Expected answer: 717/19
Correct? No
Problem: Sophia spends 40 dollars every 28 days to fill up her car's fuel tank. How much does she spend each day for her fuel?
Gemini-1.5 Pro:
Reasoning: To find out how much Sophia spends on fuel each day, divide her total fuel expense by the number of days: $40 / 28 days = $<<40/28=1.43>>1.43 per day (rounded to the nearest cent). ### Answer: $1.43 per day.
Expected answer: 10/7
Correct? No
Problem: Roberto has 50 ounces of juice. He splits the juice into 17 equal parts. He then takes the juice from one part and pours it into a container. He then takes 34/44 of what is in that container and pours it into another container. How much juice is now in the second container?
Gemini-1.5 Pro:
Reasoning: Roberto puts 50/17 ounces of juice into each container, which is 2.94 ounces. He then pours (34/44)*2.94 = <<(34/44)*2.94= 2.27>> 2.27 ounces into the second container. ### Answer: 2.27 ounces
Expected answer: 25/11
Correct? No
Problem: John wants to save some money to buy a video game. The game costs $40, but John already has $29. Every week, John is able to save 20/48 of the money he needs. After a certain period of time, he decides to put all his savings so far into an investment account. The account promises a return of 41/11 times the money invested after a year. How much money will John have in his investment account after a year?
Gemini-1.5 Pro:
Reasoning: First find how much more money John needs to save: $40 - $29 = $11. Then divide the amount John needs by his savings each week to find how many weeks it will take him to save enough: $11 / ($20/48) = 26.4 weeks. Since we only care about whole weeks, we can round this up to 27 weeks because in week 27 John will have definitively saved enough money. We know he saves $20/48 per week so over 27 weeks, he will have saved: 27 * ($20/48) = $11.25. We then multiply this amount by the return the investment account promises: $11.25 * (41/11) = $41.25 So, after one year, John will have $41.25 in his investment account. ### Answer: $41.25
Expected answer: 205/12
Correct? No
Problem: Maria starts with 13/3 euros in her pocket. She buys a candy bar that costs 32/15 euros. How much money does Maria have left?
Gemini-1.5 Pro:
Reasoning: We first need to bring the fractions to a common denominator: 13/3 is equivalent to 65/15. Therefore, Maria has 65/15 - 32/15 = 33/15 euros left. We can simplify 33/15 to 11/5. ### Answer: 11/5 euros
Expected answer: 11/5
Correct? Yes
Problem: Now, let's consider a different scenario. Suppose Maria initially starts with 36/3 euros in her pocket instead of 13/3 euros. After buying the same candy bar that costs 32/15 euros, how much money would Maria have left then?
Gemini-1.5 Pro:
Reasoning: First, we simplify 36/3, which equals 12 euros. Then we need to bring 12 to a fraction with the same denominator as 32/15: 12 is equivalent to 180/15. Finally, we subtract the price of the candy bar from Maria's initial amount: 180/15 - 32/15 = 148/15 euros. ### Answer: 148/15 euros
Expected answer: 148/15
Correct? Yes
Problem: A carpenter cuts a piece of lumber into pieces that are each 45/44 meters long. How long would 20 pieces of such lumber be in total?
Gemini-1.5 Pro:
Reasoning: The total length is 20 * 45/44 = 900/44 = 20.45 meters. ### Answer: 20.45 meters.
Expected answer: 225/11
Correct? No
Problem: A sprinter runs two sections of a race. The first part is run at a speed of 34 miles per 14 hours, and the second part is run at a speed of 21 miles per 26 hours. How much distance does the sprinter cover in one hour from both parts together?
Gemini-1.5 Pro:
Reasoning: The sprinter covers 34/14=<<34/14=2.43>>2.43 miles in one hour for the first part. The sprinter covers 21/26=<<21/26=0.81>>0.81 miles in one hour for the second part. Altogether, the sprinter covers 2.43+0.81=<<2.43+0.81=3.24>>3.24 miles in one hour. ### Answer: 3.24 miles.
Expected answer: 589/182
Correct? No
Problem: Tom has $30 in his wallet and finds $14 on the ground. Later, he gets $25 as a birthday gift. How much money does Tom have now?
Gemini-1.5 Pro:
Reasoning: Tom has $30 + $14 = $<<30+14=44>>44 after finding money on the ground. He then has $44 + $25 = $<<44+25=69>>69 after receiving his birthday gift. ### Answer: $69
Expected answer: 69
Correct? Yes
Problem: Following from the previous problem, now Tom decides to do some chores for his neighbor and earns an additional value equivalent to 37/33 dollars. How much money does Tom have now after receiving this additional amount?
Gemini-1.5 Pro:
Reasoning: We can express 37/33 dollars as a mixed number, which is 1 4/33 dollars. Adding the whole dollar amount, Tom now has $69 + $1 = $70. Adding the fractional amount to his total, Tom now has $70 + $4/33 = $70 4/33 ### Answer: $70 4/33
Expected answer: 2314/33
Correct? Yes
Problem: Jenny is on a running exercise. She ran for 41/32 miles in the first round, and then took a break. After resting, she ran for another 11/4 miles. How many miles in total did she run?
Gemini-1.5 Pro:
Reasoning: The total distance Jenny ran is 41/32 + 11/4 = 129/32 miles. ### Answer: 129/32 miles
Expected answer: 129/32
Correct? Yes
Problem: After her running exercise, Jenny decided to continue with a cycling exercise. She cycled for an additional 15 miles. What is the total distance that Jenny covered in both her running and cycling exercise?
Gemini-1.5 Pro:
Reasoning: We know Jenny ran for 129/32 miles and cycled for 15 miles. To find the total distance, we need to add these amounts: 129/32 + 15. To add these, we need a common denominator: 129/32 + 480/32 = 609/32 miles ### Answer: 609/32 miles
Expected answer: 609/32
Correct? Yes
Problem: Suppose Jenny's running exercise has changed and she ran a shorter distance during her second round. In the first round, she ran for 41/32 miles and then, after resting, she ran for another 3/4 miles in the second round. How many miles in total did she run now?
Gemini-1.5 Pro:
Reasoning: The total distance Jenny ran is 41/32 + 3/4 = 65/32 miles. ### Answer: 65/32 miles
Expected answer: 65/32
Correct? Yes
Problem: John had $32 in his wallet. He then found a $33 bill on the floor. How much money does John have now?
Gemini-1.5 Pro:
Reasoning: John's total money is the sum of his original amount and the amount he found: $32 + $33 = $65 ### Answer: $65
Expected answer: 65
Correct? Yes
Problem: Suppose that initially, John only had $3 in his wallet instead of $32 before he found the $33 bill. How much money would John have had in that case before buying the video game?
Gemini-1.5 Pro:
Reasoning: If John initially had $3 and then found $33, he would have had a total of $3 + $33 = $36. ### Answer: $36
Expected answer: 36
Correct? Yes
Problem: Carrie rode her bike for 7 hours, and then another 38/25 of an hour. If she was able to cover 35 kilometers in each hour, how many kilometers did she cover in total?
Gemini-1.5 Pro:
Reasoning: Carrie rode for a total of 7 + 38/25 = <<7+38/25=8.52>>8.52 hours. That means she covered 8.52 * 35 = <<8.52*35=298.2>>298.2 kilometers. ### Answer: 298.2 kilometers.
Expected answer: 1491/5
Correct? No
Problem: John saved $17 in January. He then added $10 more for the month of February. How much total money has he saved after February?
Gemini-1.5 Pro:
Reasoning: John's total savings after February is $17 + $10 = $<<17+10=27>>27 ### Answer: $27
Expected answer: 27
Correct? Yes
Problem: In March, John saved an additional $14. How much money does he have in total after saving in March?
Gemini-1.5 Pro:
Reasoning: John's total savings after March is $27 + $14 = $<<27+14=41>>41. ### Answer: $41
Expected answer: 41
Correct? Yes
Problem: If John initially saved $28 in January instead of $17 and added $10 more for the month of February as earlier, how much total money would he have saved after February?
Gemini-1.5 Pro:
Reasoning: John's total savings after February is $28 + $10 = $<<28+10=38>>38 ### Answer: $38
Expected answer: 38
Correct? Yes
Problem: A car travels 41 miles per hour on a trip that lasts 20/11 hours. How far did the car travel during this trip?
Gemini-1.5 Pro:
Reasoning: We can calculate the total distance traveled by multiplying the car's speed by the duration of the trip. This translates to 41 miles/hour * 20/11 hours = 820/11 miles = 74.55 miles (approximately). ### Answer: 74.55 miles (approximately)
Expected answer: 820/11
Correct? No
Problem: Tony has 38 books in his collection. If each book cost him 21 dollars, how much money did he spend in total on his book collection?
Gemini-1.5 Pro:
Reasoning: Tony spent 38 x 21 = <<38*21=798>>798 dollars in total on his book collection. ### Answer: 798 dollars
Expected answer: 798
Correct? Yes
Problem: In the previous problem, we considered that Tony has 38 books, each costing him 21 dollars. Now, consider that Tony actually spent 24 dollars on each book. How much money did Tony spend in total on his book collection now?
Gemini-1.5 Pro:
Reasoning: Tony spent 38 x 24 = <<38*24=912>>912 dollars in total on his book collection. ### Answer: 912 dollars
Expected answer: 912
Correct? Yes
Problem: Johnnie's car uses 16 liters of gas every hour. How many liters of gas would it use if he drives continuously for 19 hours?
Gemini-1.5 Pro:
Reasoning: Johnnie's car would use 16*19 = <<16*19=304>>304 liters of gas if he drives continuously for 19 hours. ### Answer: 304 liters
Expected answer: 304
Correct? Yes
Problem: Johnnie's car uses 16 liters of gas every hour. How many liters of gas would it use if he drives continuously for 19 hours? If Johnnie already had 17 liters of gas in his tank before starting the journey, how many more liters does he need to complete his drive?
Gemini-1.5 Pro:
Reasoning: Johnnie's car would use 16*19 = <<16*19=304>>304 liters of gas if he drives continuously for 19 hours. Johnnie needs 304-17 = <<304-17=287>>287 more liters of gas to complete the drive. ### Answer: 287 liters
Expected answer: 287
Correct? Yes
Problem: Johnnie's car uses 16 liters of gas every hour. In the previous problem, he was planning to drive for 19 hours. However, what if he is now planning to drive continuously for 39 hours instead? How many liters of gas would he need then?
Gemini-1.5 Pro:
Reasoning: Johnnie's car would use 16*39 = <<16*39=624>>624 liters of gas if he drives continuously for 39 hours. ### Answer: 624 liters
Expected answer: 624
Correct? Yes
Problem: Joe was tasked with distributing 40 pamphlets each day. On day 19, how many pamphlets has Joe distributed in total?
Gemini-1.5 Pro:
Reasoning: Joe has distributed 40*19 = <<40*19=760>>760 pamphlets in total. ### Answer: 760
Expected answer: 760
Correct? Yes
Problem: After distributing pamphlets for 19 days, Joe realizes he made a mistake and had to destroy 5 of the pamphlets initially considered distributed. How many pamphlets has Joe actually distributed after accounting for this error?
Gemini-1.5 Pro:
Reasoning: Joe destroyed 5 pamphlets over 19 days, meaning he destroyed 5*19 = <<5*19=95>>95 pamphlets. Accounting for the destroyed pamphlets, Joe actually distributed 760-95 = <<760-95=665>>665 pamphlets. ### Answer: 665
Expected answer: 755
Correct? No
Problem: Joe initially thought that he was supposed to distribute 40 pamphlets each day. However, he was actually supposed to distribute 27 pamphlets daily. Therefore, how many pamphlets should he have distributed after 19 days, excluding the ones he incorrectly distributed and had to destroy?
Gemini-1.5 Pro:
Reasoning: Joe should have distributed 27*19 = <<27*19=513>>513 pamphlets after 19 days. ### Answer: 513
Expected answer: 513
Correct? Yes
Problem: A farmer harvested 16/5 bushels of corn per acre. Meanwhile, the farmer has 42 acres of land but has to let 49/4 acres lie fallow. How many bushels of corn does the farmer harvest from the land that was not fallow?
Gemini-1.5 Pro:
Reasoning: The number of acres the farmer harvests from is 42-49/4 = <<42-49/4=29/4>>29/4 acres. Thus, the farmer harvests 16/5 x 29/4 = <<16/5*29/4=116/5>> 116/5 bushels of corn. ### Answer: 116/5
Expected answer: 476/5
Correct? No
Problem: Jennifer is selling lemonade for a fundraiser. Every jug she sells contains 21 gallons of lemonade. Due to evaporation, when she sells the jugs she only receives 31/34 of the volume she originally had. How much lemonade does Jennifer have after selling a full jug?
Gemini-1.5 Pro:
Reasoning: 21 gallons is equivalent to 21*34 = <<21*34=714>>714/34 gallons. After selling a jug, Jennifer loses 714/34 * (1 - 31/34) = 21/34 * 3/34 = 63/1156 gallons. Thus, Jennifer has 714/34 - 63/1156 = 23814/1156 - 63/1156 = 23751/1156 gallons left. ### Answer: 23751/1156 gallons.
Expected answer: 651/34
Correct? No
Problem: Jane cycles at a rate of 11 km/h for 45 hours. In addition to this distance, Jane also decides to cycle for another distance that equals exactly 1 km. How many kilometers in total does Jane cycle?
Gemini-1.5 Pro:
Reasoning: Jane cycles 11*45 = <<11*45=495>>495 km in 45 hours. In total, Jane cycles 495+1 = <<495+1=496>>496 km. ### Answer: 496 km
Expected answer: 496
Correct? Yes
Problem: After cycling the total distance as calculated earlier, Jane realizes she needs to get an object that is 30 km back from her current location. How many kilometers is the object from her starting point?
Gemini-1.5 Pro:
Reasoning: The object is 496-30 = <<496-30=466>>466 km away from her starting point. ### Answer: 466 km
Expected answer: 466
Correct? Yes
Problem: George had $21 in his wallet, then he found a bundle of change on the street worth $21/39. How much money does George have now?
Gemini-1.5 Pro:
Reasoning: $21/39 is equivalent to 21/39 = <<21/39=0.54>>$0.54 George has a total of $21 + $0.54 = <<21+0.54=21.54>>$21.54 ### Answer: $21.54
Expected answer: 280/13
Correct? No
Problem: John is on a bike ride. He bikes 46 miles to the town of Baker, and then another 41 miles to the town of Nelson. How many total miles did John bike?
Gemini-1.5 Pro:
Reasoning: John biked a total of 46 + 41 = <<46+41=87>>87 miles. ### Answer: 87 miles.
Expected answer: 87
Correct? Yes
Problem: After cycling a total of 46 + 41 miles, John realized that he had miscounted. Instead of cycling 46 miles to the town of Baker, he had actually cycled only 8 miles. How many total miles did John bike when he reached the town of Nelson?
Gemini-1.5 Pro:
Reasoning: John cycled 8 + 41 = <<8+41=49>>49 miles. ### Answer: 49 miles.
Expected answer: 49
Correct? Yes
Problem: John earns 4 dollars per hour at his part-time job. If he works for 9 hours, how much money does John earn in total?
Gemini-1.5 Pro:
Reasoning: John earns 4*9 = $<<4*9=36>>36 in total. ### Answer: $36
Expected answer: 36
Correct? Yes
Problem: If John and his siblings each earn 4 dollars per hour but instead of working for 9 hours they worked for 39 hours, how much does each person earns individually?
Gemini-1.5 Pro:
Reasoning: If each person works 39 hours, then each person earns 4*39 = $<<4*39=156>>156. ### Answer: $156
Expected answer: 156
Correct? Yes
Problem: Jack had 38 dollars. He then earned 41/48 of a dollar from recycling cans. The next day, he found a quarter (or 23/24 of a dollar) on the ground. How much money does Jack have now?
Gemini-1.5 Pro:
Reasoning: Jack earned 41/48 * $1 = $0.85 from recycling. Adding the quarter, Jack has $38 + $0.85 + $0.25 = $39.10 ### Answer: $39.10
Expected answer: 637/16
Correct? No
Problem: Jenny drove for a total of 29 hours at a speed of 32/24 miles per hour. How far could she travel if her speed increased by a factor of 43/15?
Gemini-1.5 Pro:
Reasoning: Jenny's original speed was 32/24 = <<32/24=1.3333333333333333>> 1.33 miles per hour. Her increased speed is (32/24)*(43/15) = <<(32/24)*(43/15)>>3.82 miles per hour. Therefore, she could travel 3.82*29 = <<3.82*29=110.78>>110.78 miles with the increased speed. ### Answer: 110.78
Expected answer: 4988/45
Correct? No
Problem: During an art class, students used liquid paint. Every child received 16/31 litres of paint. If there were 32 children in the class, what is the total amount of paint distributed to all the students?
Gemini-1.5 Pro:
Reasoning: To find the total amount of paint used, we need to multiply the amount of paint per child (16/31 liters) by the total number of children (32). So the calculation is (16/31) * 32 = 512/31 liters. ### Answer: 512/31 liters
Expected answer: 512/31
Correct? Yes
Problem: In the previous art class scenario, suppose that there were originally 40 students instead of 32. If each student still received 16/31 liters of paint initially, then what would be the total amount of paint distributed to all students initially?
Gemini-1.5 Pro:
Reasoning: To find the total initial amount of paint, we multiply the paint per student (16/31 liters) by the initial number of students (40). This gives us (16/31) * 40 = 640/31 liters. ### Answer: 640/31 liters
Expected answer: 640/31
Correct? Yes
Problem: Bob has $3 in his piggy bank. He then receives some more money, which is 3/7 of a dollar. How much money does Bob have in total?
Gemini-1.5 Pro:
Reasoning: We need to add the amount Bob received to his existing amount. That is $3 + $3/7 = $21/7 + $3/7 = $24/7 ### Answer: $24/7
Expected answer: 24/7
Correct? Yes
Problem: Bob has $3 in his piggy bank. He then receives some more money, which is 3/7 of a dollar. The next day, his grandmother sends him some additional money, exactly 29/47 of a dollar. How much money does Bob have in total now?
Gemini-1.5 Pro:
Reasoning: First find the total Bob had after receiving money, which is $3 + $3/7 = $21/7 + $3/7 = $24/7. Then add the amount his grandmother gave him: $24/7 + $29/47 = ($24 * 47 + 29 * 7)/(7*47) = $1333/329. ### Answer: $1333/329
Expected answer: 1331/329
Correct? No
Problem: Tom moved two rocks today. The first rock was moved for an interval of 20/50 hours, and the second was moved for an interval of 45/36 hours. If Tom can move rocks at a speed of 25/22 miles per hour, how far in miles did he move the rocks today?
Gemini-1.5 Pro:
Reasoning: 20/50 hours is equivalent to (20/50)*(60/1) = 24 minutes. 45/36 hours is equivalent to (45/36)*(60/1) = 75 minutes. So, Tom moved rocks for a total of 24 + 75 = 99 minutes, which is equivalent to 99/60 hours. Therefore, Tom moved the rocks a total of (25/22)*(99/60) = 1.875 miles today. ### Answer: 1.875 miles.
Expected answer: 15/8
Correct? No
Problem: A scientist mixes 10/42 liters of solution A and 32 liters of solution B to create a mixture. She then removes 4/28 liters from this mixture. If she then decides to extract 11/29 of the remaining mixture for an experiment, how much solution is she using for her experiment?
Gemini-1.5 Pro:
Reasoning: First find the total amount of solution A and solution B: 10/42 liters + 32 liters = 1354/42 liters Then subtract the amount removed: 1354/42 liters - 4/28 liters = 1334/42 liters = 667/21 liters Then multiply that number by 11/29 to find the amount used for the experiment: (667/21 liters)*(11/29) = 259/21 liters ### Answer: 259/21 liters
Expected answer: 7414/609
Correct? No
Problem: A factory produces 24 chairs in an hour. How many chairs would it produce in 25 hours?
Gemini-1.5 Pro:
Reasoning: The factory would produce 24*25 = <<24*25=600>>600 chairs in 25 hours. ### Answer: 600
Expected answer: 600
Correct? Yes
Problem: One day, the factory decides to increase its production and manufactures 24 chairs per hour for 39 hours instead of the regular 25 hours. How many chairs would be produced in these 39 hours?
Gemini-1.5 Pro:
Reasoning: The factory would produce 24*39 = <<24*39=936>>936 chairs in 39 hours. ### Answer: 936
Expected answer: 936
Correct? Yes
Problem: There are two containers of juice. The first one contains 23/35 gallon. The second one contains 50/41 gallon. After mixing the two containers of juice together, it was transferred into a bottle which can hold 28 gallons. How much space is left in the bottle after subtracting 11/19 gallon which was drunk by a customer?
Gemini-1.5 Pro:
Reasoning: * **Step 1: Find the total juice after mixing.** - Add the fractions (23/35) + (50/41) = (943/1435) + (1750/1435) = 2693/1435 gallons. * **Step 2: Calculate the remaining juice after the customer.** - Subtract the drunk amount from the total: (2693/1435) - (11/19) = (2693/1435) - (855/1435) = 1838/1435 gallons. * **Step 3: Convert gallons to a mixed number for easier comparison.** - 1838/1435 gallons is equal to 1 403/1435 gallons. * **Step 4: Determine the remaining space in the bottle.** - Since the bottle holds 28 gallons and there's a bit more than 1 gallon of juice left, the remaining space is a little less than 27 gallons. ### Answer: A little less than 27 gallons.
Expected answer: 696468/27265
Correct? No
Problem: In a bakery, they charge $47 for a regular cake. However, for custom designs, they charge an additional fee of $6 divided by the 26 available designs. What is the total cost if you decide to buy a regular cake with a custom design?
Gemini-1.5 Pro:
Reasoning: The custom design fee is $6 / 26 = $<<6/26=0.23076923076923078>>0.23 (rounded to the nearest cent). So, the total cost of the cake is $47 + $0.23 = $<<47+0.23=47.23>>47.23 ### Answer: $47.23
Expected answer: 614/13
Correct? No
Problem: John bought a drone that can fly 3 kilometers, but when it's carrying a delivery package, it can only fly 50 / 43 kilometers less. When the drone is attached with an additional booster, it can fly an additional 47 / 15 kilometers. How far can the drone fly with the package and the additional booster attached?
Gemini-1.5 Pro:
Reasoning: First find how many kilometers less the drone can fly with a package: 50 / 43 = <<50/43=1.16>>1.16 kilometers. Then subtract that number from the drone's normal flying distance to find how far it can fly with a package: 3 - 1.16 = <<3-1.16=1.84>>1.84 kilometers. Then add the additional distance the booster allows the drone to fly to find the total distance: 1.84 + 47 / 15 = <<1.84+47/15=4.97>>4.97 kilometers. ### Answer: 4.97 kilometers.
Expected answer: 3206/645
Correct? No
Problem: Ann runs 43/18 kilometers every morning and 22/9 kilometers every evening. How many kilometers does she run in a day?
Gemini-1.5 Pro:
Reasoning: Ann runs 43/18 + 22/9 = 43/18 + 44/18 = 87/18 = 29/6 kilometers in a day. ### Answer: 29/6 kilometers.
Expected answer: 29/6
Correct? Yes
Problem: Ann has set a daily goal to run 20 kilometers. If she runs 43/18 kilometers every morning and 22/9 kilometers every evening, how many more kilometers does she need to run to meet her daily goal?
Gemini-1.5 Pro:
Reasoning: Ann runs a total of 43/18 + 22/9 = 43/18 + 44/18 = 87/18 = 29/6 kilometers per day. Ann needs to run 20 - 29/6 = 120/6 - 29/6 = 91/6 kilometers more to meet her goal. ### Answer: 91/6 kilometers.
Expected answer: 91/6
Correct? Yes
Problem: In the previous question, we learned that Ann has a daily goal to run 20 kilometers. But suppose instead of running 43/18 kilometers every morning, she runs 43/12 kilometers. If she still runs 22/9 kilometers every evening, how many kilometers does she run in total each day?
Gemini-1.5 Pro:
Reasoning: First find a common denominator for 43/12 and 22/9: 12 * 3 = 36 and 9 * 4 = 36. So, Ann runs 129/36 kilometers in the morning and 88/36 kilometers in the evening. In total, she runs 129/36 + 88/36 = 217/36 kilometers each day. ### Answer: 217/36 kilometers.
Expected answer: 217/36
Correct? Yes
Problem: A car can travel 36 miles on a 1-gallon tank of gas. If the car has a 19-gallon tank, how far can it travel without needing to refuel?
Gemini-1.5 Pro:
Reasoning: The car can travel 36*19 = <<36*19=684>>684 miles with a 19-gallon tank. ### Answer: 684 miles
Expected answer: 684
Correct? Yes
Problem: The car had previously been calculated to travel 36 miles per gallon over 19 gallons. However, the measurement turned out to be incorrect and it was actually 50 miles per gallon over the same 19 gallons fuel. What would be the total distance the car could travel on a full tank with this new mileage measurement?
Gemini-1.5 Pro:
Reasoning: The car can actually travel 50*19 = <<50*19=950>>950 miles on a full tank. ### Answer: 950 miles
Expected answer: 950
Correct? Yes
Problem: John drove 18 miles each hour for 36 hours. After that, he drove an extra distance of 32/45 miles. How many miles did he drive in total?
Gemini-1.5 Pro:
Reasoning: John drove 18*36 = <<18*36=648>>648 miles in 36 hours. That means he drove a total of 648+32/45 = <<648+32/45=648.7111111111111>>648.71 miles. ### Answer: 648.71 miles
Expected answer: 29192/45
Correct? No
Problem: A car travels at a speed of 40 / 31 miles per minute. How far will it travel in 10 minutes?
Gemini-1.5 Pro:
Reasoning: The car will travel 40/31 * 10 = 400/31 miles in 10 minutes. ### Answer: 400/31 miles
Expected answer: 400/31
Correct? Yes
Problem: In contrast to the previous question, suppose the car was traveling at a different speed of 33 / 31 miles per minute instead. How far would the car travel under these new conditions in 10 minutes?
Gemini-1.5 Pro:
Reasoning: The car will travel 33/31 * 10 = 330/31 miles in 10 minutes. ### Answer: 330/31 miles
Expected answer: 330/31
Correct? Yes
Problem: John has 21 dollars and his mom gives him 11 dollars more. How much money does John have now?
Gemini-1.5 Pro:
Reasoning: We need to add the amount John's mom gave him to his original amount: $21 + $11 = $32 ### Answer: $32
Expected answer: 32
Correct? Yes
Problem: John has 21 dollars and his mom gives him 11 dollars more. Now, John's dad matches whatever amount John has. How much money does John's dad give him?
Gemini-1.5 Pro:
Reasoning: After his mom's gift, John has $21 + $11 = $32. Since John's dad matches that amount, he gives John $32. ### Answer: $32
Expected answer: 32
Correct? Yes
Problem: Samuel has $17. He finds $30 on the street. If he then converts all his money to Euros and the exchange rate is $47 to an equivalent of 33 Euros, how much money in Euros will he have now?
Gemini-1.5 Pro:
Reasoning: Samuel has a total of $17 + $30 = $47 His total amount of money is equivalent to 33 Euros because $47 is equivalent to 33 Euros. ### Answer: 33 Euros
Expected answer: 2209/33
Correct? No
Problem: Hannah has 5 piggy banks, and each piggy bank contains 34 coins. How many coins does she have in total?
Gemini-1.5 Pro:
Reasoning: Hannah has 5*34 = <<5*34=170>>170 coins in total. ### Answer: 170
Expected answer: 170
Correct? Yes
Problem: Initially, Hannah thought she had 5 piggy banks with 34 coins each. Upon recounting, she finds that she actually has 5 piggy banks with 27 coins each. How many coins does she have in the piggy banks after correcting her count?
Gemini-1.5 Pro:
Reasoning: Hannah has 5 * 27 = <<5*27=135>>135 coins in her piggy banks. ### Answer: 135
Expected answer: 135
Correct? Yes
Problem: Alex has $13/10 in his pocket. He finds $47/36 on the floor and picks it up adding to the money he already has. If he duplicates the amount of money he has by 43 times, how much money will he have?
Gemini-1.5 Pro:
Reasoning: First find the total amount of money Alex has: $13/10 + $47/36 = $(13*18)/(10*18) + $(47*5)/(36*5) = $234/180 + $235/180 = $469/180 Then multiply that amount by 43: $469/180 * 43 = $20167/180 ### Answer: $20167/180
Expected answer: 20167/180
Correct? Yes
Problem: Alex is generous. After ending up with the amount from the previous scenario, he decides to multiply his money by the original amount he ended up with after he added his pocket money to the amount he picked up from the floor. How much money does Alex end up with now?
Gemini-1.5 Pro:
Reasoning: Alex's current amount of money is $20167/180. The original amount he had was $469/180. He multiplies his current amount by his original amount: $20167/180 * $469/180 = $9456423/32400 ### Answer: $9456423/32400
Expected answer: 9458323/32400
Correct? No
Problem: John had saved 20 dollars for a new toy but accidentally lost 19 dollars. How much money does he left now?
Gemini-1.5 Pro:
Reasoning: The money left equals the initial saving minus the lost amount, which is 20 - 19 = <<20-19=1>>1 dollar. ### Answer: 1 dollar.
Expected answer: 1
Correct? Yes
Problem: Suppose that John originally had saved 26 dollars, but still lost 19 dollars. Now, how much money would he have left?
Gemini-1.5 Pro:
Reasoning: He has 26 - 19 = <<26-19=7>>7 dollars left. ### Answer: 7 dollars.
Expected answer: 7
Correct? Yes
Problem: Richard bought a bottle of wine that had 33 ounces in it. He drank 33/48 of the wine. In the morning, he drank a cup of orange juice that contained 26/30 of a liter. After a few hours, he drank a bottle of water that contained 2/36 of a liter. What is the total volume of the liquid he consumed?
Gemini-1.5 Pro:
Reasoning: * **Wine:** Richard drank (33 ounces) * (33/48) = 22.375 ounces of wine. * **Orange Juice:** A liter is approximately 33.814 ounces, so he drank (33.814 ounces) * (26/30) = 29.367 ounces of orange juice. * **Water:** He drank (33.814 ounces) * (2/36) = 1.878 ounces of water. * **Total:** In total, he drank 22.375 + 29.367 + 1.878 = 53.62 ounces of liquid. ### Answer: 53.62 ounces.
Expected answer: 16999/720
Correct? No
Problem: Jacob has $43 in his savings account and he adds $46 to his account. A few days later, he receives an additional $27/9 from his aunt. How much money does he have in his savings account now?
Gemini-1.5 Pro:
Reasoning: First find the total amount Jacob added to his account: $46 + $27/9 = $46 + $3 = $49 Then add that amount to his original savings to find his new balance: $49 + $43 = $92 ### Answer: $92
Expected answer: 92
Correct? Yes
Problem: In continuation of the above, Jacob now decides to purchase a new video game that costs $25. After purchasing the video game, what is the new balance in his savings account?
Gemini-1.5 Pro:
Reasoning: Subtract the cost of the video game from his savings balance to find his new balance: $92 - $25 = $67 ### Answer: $67
Expected answer: 67
Correct? Yes
Problem: Jacob has $35 on his gift card. He buys a toy for $22. How much money does he have left on his gift card after buying the toy?
Gemini-1.5 Pro:
Reasoning: Jacob has $35 - $22 = <<35-22=13>>13 left on his gift card after buying the toy. ### Answer: $13
Expected answer: 13
Correct? Yes
Problem: Following up on Jacob's purchase, his grandmother gives him $36 more to add to his remaining gift card balance. How much money does Jacob now have on his gift card after receiving money from his grandmother?
Gemini-1.5 Pro:
Reasoning: Jacob had $13 left on his gift card and received $36 from his grandmother, so now he has $13 + $36 = <<13+36=49>>49 on his gift card. ### Answer: $49
Expected answer: 49
Correct? Yes
Problem: Considering a variation on the previous problem, suppose Jacob initially had $35 on his gift card, but this time he decides to buy a game that costs $15 instead of the toy. How much money would he have left on his gift card after this purchase?
Gemini-1.5 Pro:
Reasoning: Jacob has $35 - $15 = <<35-15=20>>20 left on his gift card after buying the game. ### Answer: $20
Expected answer: 20
Correct? Yes
Problem: James initially had 32 dollars. He then spent 36/5 dollars on a notepad. How many dollars does he have left after his purchase?
Gemini-1.5 Pro:
Reasoning: James spent 36/5 = <<36/5=7.2>>7.2 dollars on the notepad. He has 32-7.2 = <<32-7.2=24.8>>24.8 dollars left after his purchase. ### Answer: 24.8 dollars
Expected answer: 124/5
Correct? No
Problem: Tina spent 39 dollars on groceries. Due to a discount offer, she only had to pay 16/26 of this amount. How much money did Tina pay for the groceries?
Gemini-1.5 Pro:
Reasoning: Tina paid 39*(16/26) = <<39*(16/26)=24>>24 dollars for the groceries. ### Answer: 24 dollars
Expected answer: 24
Correct? Yes
Problem: After checking her receipts carefully, Tina realized she had made another mistake. Instead of paying 16/26 of the original amount, she had actually paid 42/26. How much did she really end up paying for her groceries?
Gemini-1.5 Pro:
Reasoning: Tina paid 39*(42/26) = <<39*42/26=63>>63 dollars for the groceries. ### Answer: 63 dollars
Expected answer: 63
Correct? Yes
Problem: Jaden has $19 in his savings account. If his mother gives him $10 more, what will be the total amount in his savings account?
Gemini-1.5 Pro:
Reasoning: With the additional $10, Jaden will have $19 + $10 = $<<19+10=29>>29 in his account. ### Answer: $29
Expected answer: 29
Correct? Yes
Problem: John buys 17 pounds of apples every 8 days. He began noticing that his apples lasts about as long as 48 ounces of apple juice, which he happens to consume every 42 days. Calculate the rate of John's apple to apple juice consumption.
Gemini-1.5 Pro:
Reasoning: John consumes 17 pounds of apples every 8 days, meaning his apple consumption rate is 17 pounds / 8 days = 2.125 pounds/day. He consumes 48 oz of apple juice every 42 days, meaning his apple juice consumption rate is 48 oz / 42 days = 1.143 oz/day The ratio of John's apple to apple juice consumption rate is 2.125 pounds/day : 1.143 oz/day To simplify the ratio, we convert pounds to ounces (1 pound = 16 oz). This makes the ratio 34 oz/day : 1.143 oz/day, which simplifies to approximately 29.75 : 1. ### Answer: 29.75:1
Expected answer: 119/64
Correct? No
Problem: Maria drove her car for 8 hours at a speed of 4/7 miles per hour. In another trip, she initially had 38 dollars for gas but spent 50/4 dollars on gas. What is the summation of the total miles Maria drove and the remaining amount of money she had for gas?
Gemini-1.5 Pro:
Reasoning: * Maria drove 8*(4/7) = <<8*(4/7)=32/7>>32/7 miles. * Maria had 38 - (50/4) = <<38-(50/4)=102/4>>102/4 dollars remaining for gas. * The sum of these two numbers is (32/7) + (102/4) = <<(32/7)+(102/4)=842/28>>842/28. ### Answer: 842/28
Expected answer: 421/14
Correct? Yes
Problem: Given the earlier scenario where Maria drove for 8 hours at 4/7 miles per hour and spent 50/4 dollars from her initial 38 dollars on gas; now, Maria receives an additional $16 as a gas allowance. What is the new total value considering the distance she drove, the remaining amount of money she had for gas, and her additional gas allowance?
Gemini-1.5 Pro:
Reasoning: * Maria drove 8*(4/7) = <<8*(4/7)=32/7>>32/7 miles. * Maria had 38 - (50/4) = <<38-(50/4)=102/4>>102/4 dollars remaining for gas. * With the additional allowance, her total gas money becomes (102/4) + 16 = <<(102/4)+16 = 166/4>>166/4 dollars. * To find the total value, we need to add the distance driven, which doesn't have a monetary value, to her gas money: (32/7) + (166/4). Since 'miles' and 'dollars' are different units, we cannot directly add them. ### Answer: (32/7) miles + (166/4) dollars
Expected answer: 645/14
Correct? No
Problem: In the previous scenario where Maria drove for 8 hours, suppose her speed was slower this time, at 4/15 miles per hour. As before, she initially had 38 dollars for gas and spent 50/4 dollars on gas. Taking into account her slower speed, what is the new total considering the miles driven and the remaining amount of money Maria had for gas?
Gemini-1.5 Pro:
Reasoning: * With the slower speed, Maria drove 8*(4/15) = <<8*(4/15)=32/15>>32/15 miles. * Her remaining gas money is still 38 - (50/4) = <<38-(50/4)=102/4>>102/4 dollars. * The new total is (32/15) + (102/4) = <<(32/15)+(102/4)=1662/60>>1662/60. ### Answer: 1662/60
Expected answer: 829/30
Correct? No
Problem: A runner is training for a marathon and runs 17 miles each day. If they run the same distance for 49 days, how many miles will they have run in total?
Gemini-1.5 Pro:
Reasoning: The runner will run a total of 17*49 = <<17*49=833>>833 miles. ### Answer: 833 miles.
Expected answer: 833
Correct? Yes
Problem: The runner, still training for the marathon, now chooses a different route that is 37 miles long and runs this route for 17 days. How many miles will they have run after completing this new route for 17 days?
Gemini-1.5 Pro:
Reasoning: The runner will have run a total of 37*17= <<37*17=629>> 629 miles. ### Answer: 629 miles.
Expected answer: 629
Correct? Yes
Problem: A toy car travels 37 kilometers on a single tank of fuel. However, after a modification, the toy car can now travel an additional 33/40 of a kilometer. What is the total distance the toy car can now travel on a single tank of fuel after the modification?
Gemini-1.5 Pro:
Reasoning: First, convert the fraction 33/40 into a decimal: 33/40 = 0.825 kilometers. Then, add this additional distance to the original distance: 37 kilometers + 0.825 kilometers = 37.825 kilometers. ### Answer: 37.825 kilometers
Expected answer: 1513/40
Correct? No
Problem: John traveled for 1/31 of an hour by car and then took a bus for another 30/12 hours. After taking a short break of 17/4 hours, how long in total was John on the move?
Gemini-1.5 Pro:
Reasoning: 30/12 hours is equal to 30/12 = <<30/12=2.5>> 2.5 hours. In total, John traveled for 1/31+2.5+17/4 = <<1/31+2.5+17/4=6.79>>6.79 hours. ### Answer: 6.79 hours
Expected answer: 841/124
Correct? No
Problem: In a certain village, the well is 45 miles away. However, every hour, a donkey can carry water back from the well, effectively reducing the distance by 18/33 miles. After 1 hour, what is the effective distance of the well from the village?
Gemini-1.5 Pro:
Reasoning: The donkey reduces the effective distance by 18/33 miles each hour. Therefore, the effective distance after 1 hour is 45 - (18/33) = <<45-(18/33)=44.45>>44.45 miles. ### Answer: 44.45 miles.
Expected answer: 489/11
Correct? No
Problem: Clara had 30 dollars initially. She spent 25/6 dollars on ice cream. After buying the ice cream, she used 11/21 of her remaining money to buy a book. How many dollars did she spend on the book?
Gemini-1.5 Pro:
Reasoning: First find how much money Clara spent on ice cream: 25/6 = $<<25/6=4.17>>4.17. Then subtract the price of the ice cream from her initial amount of money to find how much money she had left: $30 - $4.17 = $<<30-4.17=25.83>>25.83. Then multiply her remaining money by 11/21 to find out how much she spent on the book: $25.83 x 11/21 = $<<25.83*11/21=13.48>>13.48 ### Answer: $13.48
Expected answer: 1705/126
Correct? No
Problem: John walked 10 miles every day for 2 weeks. After the 2 weeks, he still needed to walk an additional 21 miles to reach his destination. How many miles did he have to walk in total?
Gemini-1.5 Pro:
Reasoning: John walked 10*14 = <<10*14=140>>140 miles in two weeks because 2*7=14 days in two weeks. Therefore, he walked a total of 140+21 = <<140+21=161>>161 miles. ### Answer: 161 miles
Expected answer: 161
Correct? Yes
Problem: In the previous journey, John decided to increase his daily walking distance. He walked for 14 miles instead of 10 each day for seven weeks. After the seven weeks, he still needed to walk an additional 21 miles to reach his destination. How many miles did he have to walk this time to reach his destination?
Gemini-1.5 Pro:
Reasoning: John walked 14*7*7 = <<14*7*7=686>>686 miles in seven weeks because 7*7=49 days in seven weeks. Therefore, he walked a total of 686+21 = <<686+21=707>>707 miles. ### Answer: 707 miles
Expected answer: 707
Correct? Yes
Problem: Susan has 48 dollars in her pocket. She goes to a store and buys a toy. The toy cost is 18 dollars plus 41/14 dollars for tax. How much money does she have left after buying the toy?
Gemini-1.5 Pro:
Reasoning: First find the total cost of the tax: 41/14 = <<41/14=2.93>>2.93 dollars Then add the price of the toy and the tax to find the total cost: 2.93 + 18 = <<2.93+18=20.93>>20.93 dollars Then subtract the total cost from the amount Susan started with: 48 - 20.93 = <<48-20.93=27.07>>27.07 dollars ### Answer: 27.07 dollars
Expected answer: 379/14
Correct? No
Problem: Jamie deposited $47 in her bank account. The bank then added a bonus of 47/41 dollars to her account. How much money does Jamie now have in her bank account?
Gemini-1.5 Pro:
Reasoning: The bank added 47/41 = <<47/41=1.15>> $1.15 to her account Jamie now has 47+1.15= <<47+1.15 = 48.15>> $48.15 in her account. ### Answer: $48.15
Expected answer: 1974/41
Correct? No
Problem: Walter pays 23/21 dollars for a pen. After buying the pen, he still has 46 dollars left. How much money did he have originally?
Gemini-1.5 Pro:
Reasoning: We need to add the price of the pen to the amount of money Walter has left: 23/21 + 46 = 991/21 = <<991/21=47 4/21>>47 4/21 dollars. ### Answer: 47 4/21 dollars
Expected answer: 989/21
Correct? No
Problem: A farmer harvests honey and sells it in kilograms. In a day, the farmer on average harvests 44/10 kilograms from each beehive. If there are 37 beehives, how many kilograms honey does he harvest in a day? If he sells 3/37 of the total honey harvested in a day, how many kilograms of honey does he sell?
Gemini-1.5 Pro:
Reasoning: The farmer harvests a total of 44/10*37 = <<44/10*37=162.8>>162.8 kilograms of honey from all the beehives in a day. The farmer sells a total of 3/37*162.8 = <<3/37*162.8=13.2>>13.2 kilograms of honey in a day ### Answer: 13.2
Expected answer: 66/5
Correct? Yes
Problem: Jessica earns 29 dollars per hour. If she works for 14 hours, how much money will she have earned?
Gemini-1.5 Pro:
Reasoning: If Jessica earns $29 per hour and works 14 hours, she will have earned 29*14 = $<<29*14=406>>406. ### Answer: $406
Expected answer: 406
Correct? Yes
Problem: Jessica considers working more hours and renegotiates her hourly wage to 40 dollars per hour. If she still works for 14 hours, how much money will she have earned now?
Gemini-1.5 Pro:
Reasoning: If Jessica earns $40 per hour and works 14 hours, she will have earned 40*14 = $<<40*14=560>>560. ### Answer: $560
Expected answer: 560
Correct? Yes
Problem: Tim has a quirky old car with a very unusual fuel consumption - it uses 41/39 liters of fuel per minute. If he drives for 47 minutes, how many litres of fuel will he have consumed?
Gemini-1.5 Pro:
Reasoning: In one minute, Tim's car consumes 41/39 liters of fuel. To find out the total fuel consumption over 47 minutes, we multiply the consumption per minute by the total driving time: (41/39 liters/minute) * 47 minutes = 48.05 liters (rounded to two decimal places). ### Answer: 48.05 liters
Expected answer: 1927/39
Correct? No
Problem: A cargo ship carries 17 / 26 tons of cargo for every one of its 39 containers. It already has an existing cargo load of 50 / 11 tons. What is the total tonnage of the cargo on the ship after it loads all 39 containers?
Gemini-1.5 Pro:
Reasoning: First find the total cargo the ship takes in all 39 containers: (17 / 26) tons/container * 39 containers = 25.5 tons Then add that amount to the existing cargo load to find the total cargo weight: 25.5 tons + (50 / 11) tons = 30 tons ### Answer: 30 tons
Expected answer: 661/22
Correct? No
Problem: Jessie has $34 in savings, and then she receives $20 from her grandma. How much money does she have now?
Gemini-1.5 Pro:
Reasoning: Jessie has a total of 34 + 20 = <<34+20=54>>$54 now. ### Answer: $54
Expected answer: 54
Correct? Yes
Problem: Jessie decides to save her money for 13 weeks. Each week, she saves an amount equal to the sum of her initial savings and the money she received from her grandma. How much money does she save in total after 13 weeks?
Gemini-1.5 Pro:
Reasoning: Jessie saves $34 + $20 = $54 each week. Over 13 weeks, Jessie saves a total of $54 x 13 = $702. ### Answer: $702
Expected answer: 702
Correct? Yes
Problem: Instead of starting with $34, suppose Jessie initially had $45 in savings. She still receives $20 from her grandma. How much money does she have now?
Gemini-1.5 Pro:
Reasoning: Jessie now has a total of $45 + $20 = <<45+20=65>>$65. ### Answer: $65
Expected answer: 65
Correct? Yes
Problem: Derek has $42 saved up. His grandmother gives him an additional $7. How much money does Derek have in total now?
Gemini-1.5 Pro:
Reasoning: We need to add the amount Derek's grandmother gave him to his original savings. This means we need to calculate $42 + $7 = $<<42+7=49>>49 ### Answer: $49
Expected answer: 49
Correct? Yes
Problem: Now suppose Derek originally had $42, but his grandmother gave him $12 instead of $7. How much money does Derek have now?
Gemini-1.5 Pro:
Reasoning: Again, we need to add the money his grandmother gave him to his original savings. So, Derek now has $42 + $12 = $<<42+12=54>>54 ### Answer: $54
Expected answer: 54
Correct? Yes
Problem: A man spends 43 dollars on groceries but gets a discount of 43/27 dollars. Later, he buys a book worth 13/36 dollars. How much money did he spend in total?
Gemini-1.5 Pro:
Reasoning: * First find the discount amount: 43/27 = <<43/27=1.5925925925925926>>1.59 dollars (rounded to the nearest cent). * Then subtract the discount to find the actual grocery cost: $43 - $1.59 = $41.41 * Finally, add the cost of the book to find the total amount spent: $41.41 + $13/36 = $41.41 + $0.36 = $41.77 ### Answer: $41.77
Expected answer: 4511/108
Correct? No
Problem: Jenna has saved up $45 from her part-time job and received $50 from her parents as a gift. After she bought a novel that cost 46/39 dollars, how much money does Jenna have left?
Gemini-1.5 Pro:
Reasoning: The novel cost 46/39 = <<46/39=1.17948717949>>$1.18 (rounded to the nearest cent). Jenna had 45+50 = <<45+50=95>>$95 in total. Jenna has 95-1.18 = <<95-1.18=93.82>>$93.82 left. ### Answer: $93.82
Expected answer: 3659/39
Correct? No
Problem: You have 27/6 gallons of water in a tank. You then pour out 5/40 gallons of water from the tank. As you noticed the tank seems low, you add 21/26 gallons more. How many gallons of water are in the tank after all those actions?
Gemini-1.5 Pro:
Reasoning: Let's simplify the fractions first to make the calculations easier. * 27/6 gallons simplifies to 9/2 gallons. * 5/40 gallons simplifies to 1/8 gallons. * 21/26 gallons cannot be simplified further. Now, let's calculate the amount of water remaining after pouring out some: * 9/2 - 1/8 = 36/8 - 1/8 = 35/8 gallons Finally, let's add the amount of water poured back in: * 35/8 + 21/26 = (35*13)/(8*13) + (21*4)/(26*4) = 455/104 + 84/104 = 539/104 gallons ### Answer: 539/104 gallons
Expected answer: 539/104
Correct? Yes
Problem: Consider the same scenario as before, but this time, instead of pouring out 5/40 gallons of water from the tank, you pour out 5/19 gallons. After adding 21/26 gallons of water, how many gallons of water are in the tank now?
Gemini-1.5 Pro:
Reasoning: We will follow similar steps as before, keeping in mind that we are now pouring out 5/19 gallons instead of 5/40 gallons. * We start with 27/6 gallons, which simplifies to 9/2 gallons. * 21/26 gallons cannot be simplified further. Let's calculate the amount of water remaining after pouring out 5/19 gallons: * 9/2 - 5/19 = (9*19)/(2*19) - (5*2)/(19*2) = 171/38 - 10/38 = 161/38 gallons Finally, let's add the amount of water poured back in: * 161/38 + 21/26 = (161*13)/(38*13) + (21*19)/(26*19) = 2093/494 + 399/494 = 2492/494 gallons. This can be simplified by dividing the numerator and denominator by their greatest common factor, 2: * 2492/494 = 1246/247 gallons ### Answer: 1246/247 gallons
Expected answer: 1246/247
Correct? Yes
Problem: If a car is traveling at a steady speed of 28 miles per hour, how many miles will it travel in 20 hours?
Gemini-1.5 Pro:
Reasoning: Since the car travels 28 miles every hour, in 20 hours it will travel 28*20 = <<28*20=560>>560 miles. ### Answer: 560 miles.
Expected answer: 560
Correct? Yes
Problem: Continuing from the previous scenario, after traveling for 20 hours at a speed of 28 miles per hour, the car continues on for an additional 22 miles. How many miles has the car traveled in total?
Gemini-1.5 Pro:
Reasoning: We already know the car traveled 560 miles in the first 20 hours. Adding the additional 22 miles, the car has traveled a total of 560+22 = <<560+22 = 582>>582 miles. ### Answer: 582 miles.
Expected answer: 582
Correct? Yes
Problem: Following up from the initial scenario, suppose the car was instead traveling at a consistent speed of 28 miles per hour for 32 hours. How many miles will the car travel in this case?
Gemini-1.5 Pro:
Reasoning: Since the car travels 28 miles every hour, in 32 hours it will travel 28*32 = <<28*32=896>>896 miles. ### Answer: 896 miles.
Expected answer: 896
Correct? Yes
Problem: Tom had 48 dollars in his wallet. After he bought a book for 19 dollars, how much money does he have left?
Gemini-1.5 Pro:
Reasoning: To find out how much money Tom has left, we need to subtract the cost of the book from the amount of money he had initially. This means we need to calculate 48 - 19 = <<48-19=29>>29. ### Answer: 29 dollars
Expected answer: 29
Correct? Yes
Problem: Instead of spending 19 dollars on a book, let's say that Tom had initially spent 30 dollars on a more expensive book. How much money would Tom have left in his wallet after this purchase?
Gemini-1.5 Pro:
Reasoning: Tom started with 48 dollars and spent 30 dollars on a book. To find out how much money he has left, we subtract the cost of the book from his initial amount: 48 - 30 = <<48-30=18>>18 dollars. ### Answer: 18 dollars
Expected answer: 18
Correct? Yes
Problem: James has 19 dollars in his account. He earns 49/44 dollars per hour working online. How many dollars does he have in his account after working for an hour?
Gemini-1.5 Pro:
Reasoning: James earns $49/44 = <<49/44=1.11363636364>>$1.11 (rounded to the nearest cent) per hour. After working for an hour, he has $19 + $1.11 = <<19+1.11=20.11>>$20.11 in his account. ### Answer: $20.11
Expected answer: 885/44
Correct? No
Problem: Your favorite juice shop buys oranges for $34 per 8 bags. They've found a new vendor offering the same quantity of oranges for $19 per 30 bags. How much less per bag does the new vendor charge?
Gemini-1.5 Pro:
Reasoning: The original vendor charges $34 / 8 = $4.25 per bag. The new vendor charges $19 / 30 = $0.63 per bag (rounded to the nearest cent). The new vendor charges $4.25 - $0.63 = $3.62 less per bag. ### Answer: $3.62
Expected answer: 217/60
Correct? No
Problem: Lisa spends $50 for over 46 days. How much amount does Lisa spend per day?
Gemini-1.5 Pro:
Reasoning: Lisa spends $50/46 = $<<50/46=1.09>>1.09 per day. ### Answer: $1.09
Expected answer: 25/23
Correct? No
Problem: A bottle contains 22/43 liters of juice. If you drink 18/4 of the bottle, how many liters of juice do you drink?
Gemini-1.5 Pro:
Reasoning: Drinking 18/4 of the bottle means drinking (18/4)*(22/43) = 99/86 liters of juice. ### Answer: 99/86 liters.
Expected answer: 99/43
Correct? No
Problem: John had $31 in his wallet. He spent $4 on a chocolate bar. How much money does he have left?
Gemini-1.5 Pro:
Reasoning: If John had $31 and spent $4, he has $31 - $4 = $<<31-4=27>>27 left. ### Answer: $27
Expected answer: 27
Correct? Yes
Problem: After spending $4 on a chocolate bar from his original $31, John decided to buy a book that costs $23. How much money does he have left after buying the book?
Gemini-1.5 Pro:
Reasoning: After buying the chocolate bar, John had $27 left. After buying a book for $23, he has $27 - $23 = $<<27-23=4>>4 left. ### Answer: $4
Expected answer: 4
Correct? Yes
Problem: A sports car travels at a speed of 40 miles per hour on a highway. Additional to that, it gains an extra speed of 26/24 miles every hour due to a powerful wind from behind. What would be its speed after one hour with the effect of the wind included?
Gemini-1.5 Pro:
Reasoning: First, simplify the fraction representing the speed increase from the wind: 26/24 = 13/12 miles per hour. Next, add this speed increase to the car's initial speed: 40 + 13/12 = 480/12 + 13/12 = 493/12 miles per hour. ### Answer: 493/12 miles per hour.
Expected answer: 493/12
Correct? Yes
Problem: In the previous scenario, where a sports car was traveling on the highway, suppose instead that it initially travels at a speed of 40 miles per hour. However, now it gains an extra speed of 6/24 miles every hour due to a change in the wind's strength. What would be its speed after one hour, considering the new effects of the wind?
Gemini-1.5 Pro:
Reasoning: We begin by simplifying the fraction representing the additional speed from the wind: 6/24 = 1/4 miles per hour. Next, we add this speed increase to the car's initial speed: 40 + 1/4 = 160/4 + 1/4 = 161/4 miles per hour. ### Answer: 161/4 miles per hour.
Expected answer: 161/4
Correct? Yes
Problem: James bought a jug of milk which contains 33/37 gallons. Later, he decided to add more milk into the jug, which was 3/25 gallons. How many gallons of milk does James have in total in the jug?
Gemini-1.5 Pro:
Reasoning: To add the fractions, we need to find a common denominator for 37 and 25, which is 925. We can rewrite 33/37 as (33 * 25) / (37 * 25) = 825/925. We can rewrite 3/25 as (3 * 37) / (25 * 37) = 111/925. Therefore, James has a total of 825/925 + 111/925 = 936/925 gallons of milk. ### Answer: 936/925 gallons
Expected answer: 936/925
Correct? Yes
Problem: In the previous problem, James had a jug containing 33/37 gallons of milk to which he added an extra 3/25 gallons. Now, suppose James had 30 similar jugs of milk, each with the same combined volume as the first. What would be the total amount of milk in gallons for all 30 jugs?
Gemini-1.5 Pro:
Reasoning: We know from the previous problem that one jug contains 936/925 gallons of milk. Therefore, 30 jugs would contain 30 * (936/925) = 28080/925 gallons of milk. This fraction can be simplified to 30 330/925, which simplifies further to 30 66/185. ### Answer: 30 66/185 gallons
Expected answer: 5616/185
Correct? Yes
Problem: In the previous problems, James had a jug containing 33/37 gallons of milk to which he added an extra 3/25 gallons. Now, suppose instead of adding 3/25 gallons of milk, he added 42/25 gallons. How many gallons of milk does James have in total in the jug now?
Gemini-1.5 Pro:
Reasoning: We need to add 33/37 and 42/25. First, we find a common denominator for 37 and 25, which is 925. We can rewrite 33/37 as (33 * 25) / (37 * 25) = 825/925. We can rewrite 42/25 as (42 * 37) / (25 * 37) = 1554/925. Therefore, James has a total of 825/925 + 1554/925 = 2379/925 gallons of milk. ### Answer: 2379/925 gallons
Expected answer: 2379/925
Correct? Yes
Problem: A journey took 43/17 hours to complete. After the journey, a break of 31/4 hours was taken. What is the total time spent on the journey and the break?
Gemini-1.5 Pro:
Reasoning: To find the total time, we need to add the journey time and the break time: 43/17 + 31/4 First find a common denominator: The least common multiple of 17 and 4 is 68. So, we convert both fractions to have a denominator of 68: (43/17)*(4/4) + (31/4)*(17/17) = 172/68 + 527/68 Now we can add the fractions: 172/68 + 527/68 = 699/68 ### Answer: 699/68 hours
Expected answer: 699/68
Correct? Yes
Problem: Continuing from the previous journey, if a further segment of the journey was undertaken that took an additional 50 hours, what is the total time spent on all segments of the journey and the break?
Gemini-1.5 Pro:
Reasoning: We need to add the time of the further journey segment (50 hours) to the total time of the previous journey and break (699/68 hours). First, convert 50 hours to a fraction with a denominator of 68: 50/1 * 68/68 = 3400/68 Now we can add the times: 699/68 + 3400/68 = 4099/68 hours ### Answer: 4099/68 hours
Expected answer: 4099/68
Correct? Yes
Problem: Continuing from the original journey, suppose the first segment of the journey only took 43/29 hours instead of the 43/17 hours initially stated. Keeping the break time the same at 31/4 hours, what would now be the total time spent on all parts of the journey and the break?
Gemini-1.5 Pro:
Reasoning: We need to add the new journey time (43/29 hours) and the break time (31/4 hours): 43/29 + 31/4. First, find a common denominator: The least common multiple of 29 and 4 is 116. We convert both fractions to have a denominator of 116: (43/29)*(4/4) + (31/4)*(29/29) = 172/116 + 899/116 Now we can add the fractions: 172/116 + 899/116 = 1071/116 ### Answer: 1071/116 hours
Expected answer: 1071/116
Correct? Yes
Problem: Carrie's car consumes 41 liters of fuel to travel 1 hour. If she has driven for 49/48 hours, how much fuel has her car consumed?
Gemini-1.5 Pro:
Reasoning: Carrie's car consumes 41*(49/48) = <<41*(49/48)=41.77>>41.77 liters of fuel for 49/48 hours. ### Answer: 41.77 liters
Expected answer: 2009/48
Correct? No
Problem: Oscar has $33 saved up. He decides to spend 13/41 of his money on a new video game. How much money does he spend on the video game?
Gemini-1.5 Pro:
Reasoning: Oscar spends 13/41 * $33 = $<<13/41*33=10.5>>10.5 on a new video game. ### Answer: $10.5
Expected answer: 429/41
Correct? No
Problem: A turtle travels at a speed of 19/6 feet per second. How far, in feet, would the turtle travel in 24 seconds if it starts 20 feet ahead from the starting point?
Gemini-1.5 Pro:
Reasoning: The turtle travels (19/6)*24 = <<(19/6)*24=76>>76 feet in 24 seconds. Since the turtle starts 20 feet ahead, it will have traveled 76+20 = <<76+20=96>>96 feet from the starting point. ### Answer: 96 feet.
Expected answer: 96
Correct? Yes
Problem: In our earlier calculation, we were considering the distance the turtle travelled in 24 seconds. What happens if we reconsider, and instead calculate the turtle's distance covered in 33 seconds from the same starting point that was 20 feet ahead? How many feet would the turtle travel in total then?
Gemini-1.5 Pro:
Reasoning: In 33 seconds, the turtle travels (19/6)*33 = <<(19/6)*33=104.5>>104.5 feet. Adding the 20 feet head start, the turtle would travel a total of 104.5+20 = <<104.5+20=124.5>>124.5 feet. ### Answer: 124.5 feet.
Expected answer: 249/2
Correct? No
Problem: Carlos has a container with a capacity of 3 liters. He filled it with orange juice to just 41/49 of its capacity. How many liters of orange juice did he pour into the container?
Gemini-1.5 Pro:
Reasoning: Carlos filled 41/49 * 3 = <<41/49*3=123/49>>123/49 liters of orange juice in the container. Converting 123/49 to a mixed number, we get 2 25/49. ### Answer: 2 25/49 liters.
Expected answer: 123/49
Correct? Yes
Problem: Suppose that Carlos initially had a larger container, with a capacity of 32 liters. If he still filled it to just 41/49 of its capacity with orange juice, how many liters of orange juice did he pour into this larger container?
Gemini-1.5 Pro:
Reasoning: Carlos filled 41/49 * 32 = <<41/49*32=1312/49>> 1312/49 liters of orange juice in the larger container. Converting 1312/49 to a mixed number, we get 26 38/49. ### Answer: 26 38/49 liters.
Expected answer: 1312/49
Correct? Yes
Problem: If a train travels at the speed of 39 kilometers per hour, how far would the train cover in 5 hours?
Gemini-1.5 Pro:
Reasoning: To find the distance the train covers in 5 hours, we multiply the train's speed by the time travelled: 39 * 5 = <<39*5=195>>195 kilometers. ### Answer: 195 kilometers.
Expected answer: 195
Correct? Yes
Problem: If the train was initially traveling at a speed of 16 kilometers per hour instead of 39 kilometers per hour, how far would the train have travelled in 5 hours?
Gemini-1.5 Pro:
Reasoning: Similar to before, we multiply the train's initial speed by the time traveled: 16 * 5 = <<16*5=80>>80 kilometers. ### Answer: 80 kilometers.
Expected answer: 80
Correct? Yes
Problem: Jenny has $3. She then finds a rare coin that is worth 4/37 dollars. How much money does she have altogether?
Gemini-1.5 Pro:
Reasoning: We need to add the value of the coin to Jenny's initial amount: $3 + $4/37 To make the addition easier, we can express $3 as a fraction with a denominator of 37: $3 = $111/37. Now we can add the fractions: $111/37 + $4/37 = $115/37 ### Answer: $115/37
Expected answer: 115/37
Correct? Yes
Problem: Henry saved $17 each week. How much money did Henry save in 5 weeks?
Gemini-1.5 Pro:
Reasoning: Henry saved $17 x 5 = $<<17*5=85>>85 in 5 weeks. ### Answer: $85
Expected answer: 85
Correct? Yes
Problem: Imagine if instead of saving $17 each week, Henry was actually saving $37 each week. How much money would Henry save in 5 weeks?
Gemini-1.5 Pro:
Reasoning: Henry would save $37 x 5 = $<<37*5=185>>185 in 5 weeks. ### Answer: $185
Expected answer: 185
Correct? Yes
Problem: You have $15 in your savings account. You decided to spend 17/23 of a dollar on a small sweet. How much is left in your savings account after buying the sweet?
Gemini-1.5 Pro:
Reasoning: You spent 17/23 * $1 = $0.74 on the sweet (rounded to the nearest cent). You have $15 - $0.74 = $14.26 left in your savings account. ### Answer: $14.26
Expected answer: 328/23
Correct? No