Common Core Standard 3.OA.C.7
This standard covers the following:
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 Γ 5 = 40, one knows 40 Γ· 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Problem: On a slide, for each 1 meter of sliding, Isaac gains 3 times the speed. If Isaac slides down 1 meter, how much speed does he gain?
GPT-4o:
To determine how much speed Isaac gains when he slides down 1 meter, we need to use the given information that for each 1 meter of sliding, Isaac gains 3 times the speed. Since Isaac slides down 1 meter, he gains: \[ 3 \times 1 = 3 \] ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: In light of the original problem, suppose for each 1 meter of sliding, Isaac now gains 5 times the speed instead of 3 times the speed. In this case, how much speed does he gain after sliding 1 meter?
GPT-4o:
Given the new condition that for each 1 meter of sliding, Isaac gains 5 times the speed, we need to calculate the speed gain for sliding 1 meter. Since Isaac slides down 1 meter, he gains: \[ 5 \times 1 = 5 \] ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: In the forest, for every 9 brown bears there are 11 times as many black bears. If there are 9 brown bears, how many black bears are there in the forest?
GPT-4o:
To determine the number of black bears in the forest, we start by noting that for every 9 brown bears, there are 11 times as many black bears. Given: - Number of brown bears = 9 - Ratio of black bears to brown bears = 11 times We calculate the number of black bears by multiplying the number of brown bears by the ratio: \[ \text{Number of black bears} = 9 \times 11 \] \[ \text{Number of black bears} = 99 \] ### Answer: 99
Expected answer: 99
Correct? Yes
Problem: In a particular pond, there are 7 fish. If each fish has 2 sides, how many fish sides are there in total in the pond?
GPT-4o:
To determine the total number of fish sides in the pond, we need to multiply the number of fish by the number of sides each fish has. Given: - Number of fish = 7 - Number of sides per fish = 2 Calculation: \[ \text{Total number of fish sides} = \text{Number of fish} \times \text{Number of sides per fish} \] \[ \text{Total number of fish sides} = 7 \times 2 \] \[ \text{Total number of fish sides} = 14 \] ### Answer: 14
Expected answer: 14
Correct? Yes
Problem: In an experiment, it is determined that the fuel needed for a rocket is a product of the mass of that rocket and 12. If the mass of the rocket is 8, how much fuel is needed for the rocket?
GPT-4o:
To determine the amount of fuel needed for the rocket, we use the given relationship that the fuel needed is the product of the mass of the rocket and 12. Given: - Mass of the rocket = 8 - Fuel needed per unit mass = 12 We calculate the fuel needed as follows: \[ \text{Fuel needed} = \text{Mass of the rocket} \times 12 \] \[ \text{Fuel needed} = 8 \times 12 \] \[ \text{Fuel needed} = 96 \] ### Answer: 96
Expected answer: 96
Correct? Yes
Problem: In a further experiment, a third rocket with the same mass of 8 is tested, but this time it is equipped with an improved fuel system that requires less fuel. Now, this rocket requires only 5 units of fuel per mass. How much fuel is this third rocket going to need?
GPT-4o:
To determine the amount of fuel needed for the third rocket with the improved fuel system, we use the given relationship that the fuel needed is the product of the mass of the rocket and 5 units of fuel per mass. Given: - Mass of the rocket = 8 - Fuel needed per unit mass = 5 We calculate the fuel needed as follows: \[ \text{Fuel needed} = \text{Mass of the rocket} \times 5 \] \[ \text{Fuel needed} = 8 \times 5 \] \[ \text{Fuel needed} = 40 \] ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: Theresa planted 80 flower seeds evenly among 10 plots. This means each plot received a certain amount of flower seeds. If she later planted an extra plot with the same amount of seeds as in each of the previous plots, how many seeds did she use for the extra plot?
GPT-4o:
First, we need to determine how many flower seeds were planted in each of the original 10 plots. To do this, we divide the total number of seeds by the number of plots: \[ \frac{80 \text{ seeds}}{10 \text{ plots}} = 8 \text{ seeds per plot} \] Next, we need to find out how many seeds were used for the extra plot. Since the extra plot received the same amount of seeds as each of the previous plots, it also received 8 seeds. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: In addition to planting seeds in the plots, Theresa wanted to give 7 gift bags each containing as many seeds as the number she planted in each plot. How many seeds should Theresa set aside for the gift bags?
GPT-4o:
We already know that each plot received 8 seeds. Theresa wants to give 7 gift bags, each containing the same number of seeds as in each plot. To find out how many seeds she needs for the gift bags, we multiply the number of seeds per plot by the number of gift bags: \[ 8 \text{ seeds per plot} \times 7 \text{ gift bags} = 56 \text{ seeds} \] ### Answer: 56
Expected answer: 56
Correct? Yes
Problem: In a change of plans, Theresa divided the 80 seeds evenly between only 2 plots instead of 10. This meant each plot now received a different number of seeds than before. If she later planted an extra plot with the same amount of seeds as in each of the new plots, how many seeds did she use for the extra plot?
GPT-4o:
First, we need to determine how many flower seeds were planted in each of the 2 plots. To do this, we divide the total number of seeds by the number of plots: \[ \frac{80 \text{ seeds}}{2 \text{ plots}} = 40 \text{ seeds per plot} \] Next, we need to find out how many seeds were used for the extra plot. Since the extra plot received the same amount of seeds as each of the new plots, it also received 40 seeds. ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: A dress needs 1 yard of fabric for 1 section. How many yards of fabric are needed to make that section of the dress?
GPT-4o:
To determine how many yards of fabric are needed to make one section of the dress, we simply use the given information that 1 yard of fabric is required for 1 section. ### Answer: 1 yard
Expected answer: 1
Correct? Yes
Problem: Going back to the first part of the previous problem, suppose that each section of the dress actually requires 6 yards of fabric instead of 1. How many yards of fabric are needed for one section of the dress in this case?
GPT-4o:
Given that each section of the dress now requires 6 yards of fabric, we simply use this information to determine the amount of fabric needed for one section. ### Answer: 6 yards
Expected answer: 6
Correct? Yes
Problem: Captain Blackbeard buries 11 treasure chests in a secret underground cave. To keep the treasure safe, he creates a magical spell that triples the amount of treasure chests inside the cave. How many treasure chests will be in the cave after the spell is cast?
GPT-4o:
To determine the number of treasure chests in the cave after Captain Blackbeard's spell is cast, we need to triple the initial number of treasure chests. Initially, there are 11 treasure chests. The spell triples this amount: \[ 11 \times 3 = 33 \] Therefore, after the spell is cast, there will be 33 treasure chests in the cave. ### Answer: 33
Expected answer: 33
Correct? Yes
Problem: Remembering his magical spell, Captain Blackbeard starts to second guess himself. What if his magical spell had only doubled the amount of treasure chests instead of tripling? How many treasure chests would be in the cave in that case, after the spell is cast?
GPT-4o:
To determine the number of treasure chests in the cave if the spell had only doubled the initial amount, we need to multiply the initial number of treasure chests by 2. Initially, there are 11 treasure chests. If the spell doubles this amount: \[ 11 \times 2 = 22 \] Therefore, if the spell had only doubled the amount of treasure chests, there would be 22 treasure chests in the cave. ### Answer: 22
Expected answer: 22
Correct? Yes
Problem: If a baby giraffe grows by 4 feet every year, how tall would the giraffe be after 11 years?
GPT-4o:
To determine how tall the baby giraffe would be after 11 years, we need to multiply the annual growth rate by the number of years. The baby giraffe grows by 4 feet every year. Therefore, after 11 years, the total growth would be: \[ 4 \text{ feet/year} \times 11 \text{ years} = 44 \text{ feet} \] ### Answer: 44 feet
Expected answer: 44
Correct? Yes
Problem: If instead the baby giraffe grows by 4 feet every year, how tall would the giraffe be after 7 years?
GPT-4o:
To determine how tall the baby giraffe would be after 7 years, we need to multiply the annual growth rate by the number of years. The baby giraffe grows by 4 feet every year. Therefore, after 7 years, the total growth would be: \[ 4 \text{ feet/year} \times 7 \text{ years} = 28 \text{ feet} \] ### Answer: 28 feet
Expected answer: 28
Correct? Yes
Problem: Pete has 4 pieces of rope. If each piece of rope is 8 feet long, how many feet of rope does Pete have in total?
GPT-4o:
To find the total length of rope Pete has, we need to multiply the number of pieces of rope by the length of each piece. Pete has 4 pieces of rope, and each piece is 8 feet long. Therefore, we calculate: \[ 4 \text{ pieces} \times 8 \text{ feet per piece} = 32 \text{ feet} \] So, Pete has a total of 32 feet of rope. ### Answer: 32 feet
Expected answer: 32
Correct? Yes
Problem: After examining his ropes, Pete figures out that he needs to use all of his rope for a project. If he combines all 4 pieces of his 8 foot long ropes, how many feet of rope will he have for his project?
GPT-4o:
To determine the total length of rope Pete will have for his project, we need to combine all 4 pieces of his 8-foot long ropes. We already know that each piece of rope is 8 feet long, and Pete has 4 pieces. Therefore, we calculate: \[ 4 \text{ pieces} \times 8 \text{ feet per piece} = 32 \text{ feet} \] So, Pete will have 32 feet of rope for his project. ### Answer: 32 feet
Expected answer: 32
Correct? Yes
Problem: Upon rechecking his inventory, Pete realizes he actually has 12 pieces of rope not 4. If each of these 12 ropes are 8 feet each, how much total length of rope does Pete have now?
GPT-4o:
To find the total length of rope Pete has with the updated inventory, we need to multiply the number of pieces of rope by the length of each piece. Pete now has 12 pieces of rope, and each piece is 8 feet long. Therefore, we calculate: \[ 12 \text{ pieces} \times 8 \text{ feet per piece} = 96 \text{ feet} \] So, Pete has a total of 96 feet of rope. ### Answer: 96 feet
Expected answer: 96
Correct? Yes
Problem: In the Marine Institute, there are 81 starfish. If these starfish are equally distributed in 9 tanks, how many starfish will be placed in each tank?
GPT-4o:
To determine how many starfish will be placed in each tank, we need to divide the total number of starfish by the number of tanks. Given: - Total number of starfish = 81 - Number of tanks = 9 We perform the division: \[ \frac{81}{9} = 9 \] So, each tank will have 9 starfish. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Earlier, we learned the Marine Institute distributed 81 starfish equally across 9 tanks. But what if they had only 12 starfish instead? How many starfish would equal distribution across the 9 tanks result in then?
GPT-4o:
To determine how many starfish will be placed in each tank if there are only 12 starfish, we need to divide the total number of starfish by the number of tanks. Given: - Total number of starfish = 12 - Number of tanks = 9 We perform the division: \[ \frac{12}{9} = \frac{4}{3} \approx 1.33 \] So, each tank will have approximately 1.33 starfish, but since we can't have a fraction of a starfish in practical terms, it means some tanks will have 1 starfish and others will have 2 starfish to distribute them as evenly as possible. ### Answer: 1.33
Expected answer: 4/3
Correct? No
Problem: In a sandbox, Lisa found a toy. If she finds twice as many toys every next day, how many toys will she find on the second day?
GPT-4o:
To determine how many toys Lisa will find on the second day, we need to know how many toys she found on the first day. Let's assume she found \( x \) toys on the first day. Since she finds twice as many toys every next day, on the second day she will find \( 2 \times x \) toys. If we assume \( x = 1 \) (as a simple example), then on the second day she will find: \[ 2 \times 1 = 2 \] However, without the specific number of toys found on the first day, we can only express the answer in terms of \( x \). ### Answer: \( 2x \) (where \( x \) is the number of toys found on the first day).
Expected answer: 2
Correct? Yes
Problem: After finding toys in the sandbox for two days, Lisa decides to bury and later dig up the exact square of the number of toys she found on the second day. How many toys will Lisa bury and dig up if she follows this plan?
GPT-4o:
To determine how many toys Lisa will bury and dig up, we need to know the number of toys she found on the second day. From the previous problem, we know that if Lisa finds \( x \) toys on the first day, she will find \( 2x \) toys on the second day. Lisa decides to bury and later dig up the exact square of the number of toys she found on the second day. Therefore, we need to calculate the square of \( 2x \). The square of \( 2x \) is: \[ (2x)^2 = 4x^2 \] So, Lisa will bury and dig up \( 4x^2 \) toys. ### Answer: \( 4x^2 \) (where \( x \) is the number of toys found on the first day).
Expected answer: 4
Correct? Yes
Problem: Instead of finding twice as many toys as the previous day, Lisa now finds ten times as many toys as the previous day. How many toys will she find on the second day following this new rule?
GPT-4o:
To determine how many toys Lisa will find on the second day under the new rule, we need to know how many toys she found on the first day. Let's assume she found \( x \) toys on the first day. Since she finds ten times as many toys every next day, on the second day she will find \( 10 \times x \) toys. If we assume \( x = 1 \) (as a simple example), then on the second day she will find: \[ 10 \times 1 = 10 \] However, without the specific number of toys found on the first day, we can only express the answer in terms of \( x \). ### Answer: \( 10x \) (where \( x \) is the number of toys found on the first day).
Expected answer: 10
Correct? Yes
Problem: A robot can process information in 11 microseconds, but it has to be divided by 11 to match the system's speed. How quickly can the robot process information to match the system's speed?
GPT-4o:
To determine how quickly the robot can process information to match the system's speed, we need to divide the robot's processing time by 11. Given: - The robot processes information in 11 microseconds. Calculation: \[ \text{Processing time to match system's speed} = \frac{11 \text{ microseconds}}{11} \] \[ \text{Processing time to match system's speed} = 1 \text{ microsecond} \] ### Answer: 1 microsecond
Expected answer: 1
Correct? Yes
Problem: Given that the robot processed information to match the system's speed, it needed to multiply this new processing speed by itself to calculate its efficiency rate. What is the robot's efficiency rate?
GPT-4o:
To find the robot's efficiency rate, we need to multiply the new processing speed by itself. Given: - The new processing speed is 1 microsecond. Calculation: \[ \text{Efficiency rate} = 1 \text{ microsecond} \times 1 \text{ microsecond} \] \[ \text{Efficiency rate} = 1 \text{ microsecond}^2 \] ### Answer: 1 microsecondΒ²
Expected answer: 1
Correct? Yes
Problem: If the robot's processing speed were slightly faster and instead was able to process information in 12 microseconds which still needed to be divided by 11 to match the system's speed, how quickly could the robot process information to match the system's speed then?
GPT-4o:
To determine the new processing time to match the system's speed, we need to divide the robot's new processing time by 11. Given: - The robot processes information in 12 microseconds. Calculation: \[ \text{Processing time to match system's speed} = \frac{12 \text{ microseconds}}{11} \] \[ \text{Processing time to match system's speed} \approx 1.09 \text{ microseconds} \] ### Answer: 1.09 microseconds
Expected answer: 12/11
Correct? No
Problem: Each tomato seed will produce 3 tomatoes. If Nina plants 6 tomato seeds, how many tomatoes will she produce in total?
GPT-4o:
To determine the total number of tomatoes Nina will produce, we need to multiply the number of tomato seeds she plants by the number of tomatoes each seed will produce. Nina plants 6 tomato seeds, and each seed produces 3 tomatoes. Therefore, we calculate: \[ 6 \text{ seeds} \times 3 \text{ tomatoes per seed} = 18 \text{ tomatoes} \] ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: Each of these tomatoes will produce 3 new seeds of its own. Using all the seeds from the tomatoes that Nina grows, how many new tomato plants could she potentially grow?
GPT-4o:
To determine how many new tomato plants Nina could potentially grow, we need to calculate the total number of seeds produced by the tomatoes and then see how many plants these seeds can produce. From the previous problem, we know that Nina will produce 18 tomatoes. Each of these tomatoes will produce 3 new seeds. Therefore, the total number of seeds produced is: \[ 18 \text{ tomatoes} \times 3 \text{ seeds per tomato} = 54 \text{ seeds} \] Since each seed can grow into one new tomato plant, Nina could potentially grow 54 new tomato plants. ### Answer: 54
Expected answer: 54
Correct? Yes
Problem: An alien is learning the human language. For every human word, they can transmit it to their spaceship 11 times per minute. How many words will the alien be able to transmit after 1 minute if they learn a new word?
GPT-4o:
To determine how many words the alien can transmit in 1 minute, we need to consider the given rate of transmission. The alien can transmit each word 11 times per minute. Since the alien learns a new word and can transmit it 11 times in one minute, the total number of words transmitted in that minute is simply 11. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: In the above problem, the alien learned another new word. If they transmit each word 11 times per minute and the alien can now transmit two words, how many transmissions will the alien be able to make after 1 minute?
GPT-4o:
If the alien can transmit each word 11 times per minute and now knows two words, we need to calculate the total number of transmissions for both words. For each word: - The alien transmits 11 times per minute. Since the alien knows two words: - The total number of transmissions in 1 minute is \( 11 \times 2 \). Calculating this: \[ 11 \times 2 = 22 \] ### Answer: 22
Expected answer: 22
Correct? Yes
Problem: In the previous problem, instead of transmitting each word 11 times per minute, suppose the alien can only transmit each word 3 times per minute. How many transmissions will the alien be able to make after 1 minute if they learn a new word?
GPT-4o:
To determine how many transmissions the alien can make in 1 minute, we need to consider the new rate of transmission. The alien can now transmit each word 3 times per minute. Since the alien learns a new word and can transmit it 3 times in one minute, the total number of transmissions in that minute is simply 3. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: A unicorn travels 35 miles over 7 hours. How many miles does the unicorn travel in one hour?
GPT-4o:
To determine how many miles the unicorn travels in one hour, we need to divide the total distance traveled by the total time taken. The unicorn travels 35 miles over 7 hours. Therefore, we calculate the distance traveled in one hour as follows: \[ \text{Distance per hour} = \frac{\text{Total distance}}{\text{Total time}} = \frac{35 \text{ miles}}{7 \text{ hours}} \] \[ \text{Distance per hour} = 5 \text{ miles per hour} \] ### Answer: 5 miles per hour
Expected answer: 5
Correct? Yes
Problem: If the unicorn maintains the same speed, how many miles would it travel in 3 hours?
GPT-4o:
To determine how many miles the unicorn would travel in 3 hours at the same speed, we use the speed calculated previously, which is 5 miles per hour. We multiply the speed by the time: \[ \text{Distance} = \text{Speed} \times \text{Time} = 5 \text{ miles per hour} \times 3 \text{ hours} \] \[ \text{Distance} = 15 \text{ miles} \] ### Answer: 15 miles
Expected answer: 15
Correct? Yes
Problem: If instead the unicorn traveled 35 miles in 2 hours, how many miles would the unicorn travel in one hour?
GPT-4o:
To determine how many miles the unicorn travels in one hour when it travels 35 miles in 2 hours, we need to divide the total distance by the total time. The unicorn travels 35 miles over 2 hours. Therefore, we calculate the distance traveled in one hour as follows: \[ \text{Distance per hour} = \frac{\text{Total distance}}{\text{Total time}} = \frac{35 \text{ miles}}{2 \text{ hours}} \] \[ \text{Distance per hour} = 17.5 \text{ miles per hour} \] ### Answer: 17.5 miles per hour
Expected answer: 35/2
Correct? No
Problem: Superhero Green Gauntlet has the ability to multiply his strength by a factor of 3. If Jetstream, another superhero, has 5 times the strength of Green Gauntlet, what is the strength of Jetstream?
GPT-4o:
Let's denote Green Gauntlet's initial strength as \( S \). Given that Jetstream has 5 times the strength of Green Gauntlet, we can express Jetstream's strength as: \[ \text{Jetstream's strength} = 5S \] Therefore, Jetstream's strength is 5 times the initial strength of Green Gauntlet. ### Answer: 5S
Expected answer: 15
Correct? No
Problem: Jason is stringing beads onto a necklace. If each necklace requires 6 beads, how many beads will be needed to make 1 necklace?
GPT-4o:
To determine how many beads are needed to make one necklace, we simply need to know the number of beads required per necklace. According to the problem, each necklace requires 6 beads. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: Jason had made one necklace requiring 6 beads, but now he wants to make a total of 3 necklaces. How many beads will he need in total to make these 3 necklaces?
GPT-4o:
To find out how many beads Jason will need to make 3 necklaces, we need to multiply the number of beads required for one necklace by the total number of necklaces he wants to make. Each necklace requires 6 beads. Therefore, for 3 necklaces: \[ 6 \text{ beads/necklace} \times 3 \text{ necklaces} = 18 \text{ beads} \] ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: In the original problem, Jason made one necklace using 6 beads. But what if he wanted to use a new design that requires 8 times as many beads as his original design? How many beads would Jason need to create this new necklace?
GPT-4o:
To determine how many beads Jason would need for the new design, we need to multiply the number of beads required for the original design by 8. The original design requires 6 beads. Therefore, the new design will require: \[ 6 \text{ beads} \times 8 = 48 \text{ beads} \] ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A puzzle box indicates that you need to multiply 2 by 3 to unlock it. What is the unlock code for the puzzle box?
GPT-4o:
To find the unlock code for the puzzle box, we need to multiply 2 by 3. \[ 2 \times 3 = 6 \] ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: After successfully unlocking the puzzle box with the code obtained by multiplying 2 by 3, a new challenge appears on the screen inside the box. It tells you to multiply the previous code by 12 to get the final secret code to complete the puzzle. What is the final code?
GPT-4o:
To find the final secret code, we need to multiply the previous code (which is 6) by 12. \[ 6 \times 12 = 72 \] ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: After completing the previous challenge, another puzzle appears on the next screen inside the box. It instructs you to multiply 2 by 7 instead of 3. What number will you get by following this new instruction for the puzzle?
GPT-4o:
To solve the new puzzle, we need to multiply 2 by 7. \[ 2 \times 7 = 14 \] ### Answer: 14
Expected answer: 14
Correct? Yes
Problem: Peter has 6 different wallets and in each wallet, he has 9 dollars. If he stacks all the money in one wallet, how much money will be in that wallet?
GPT-4o:
To determine how much money Peter will have if he combines all the money from his 6 wallets into one, we need to multiply the amount of money in each wallet by the number of wallets. Peter has 6 wallets, and each wallet contains 9 dollars. Therefore, we calculate the total amount of money as follows: \[ 6 \text{ wallets} \times 9 \text{ dollars per wallet} = 54 \text{ dollars} \] ### Answer: 54 dollars
Expected answer: 54
Correct? Yes
Problem: If Peter then puts all of the money from the one wallet into a piggy bank, how much money will be in the piggy bank?
GPT-4o:
If Peter puts all of the money from the one wallet, which contains 54 dollars, into a piggy bank, then the amount of money in the piggy bank will be the same as the amount in the wallet. ### Answer: 54 dollars
Expected answer: 54
Correct? Yes
Problem: If Peter originally had 12 dollars in each of the 6 wallets instead of 9, how much money would be in the one wallet then?
GPT-4o:
To determine how much money Peter would have if he combined all the money from his 6 wallets into one, given that each wallet originally had 12 dollars, we need to multiply the amount of money in each wallet by the number of wallets. Peter has 6 wallets, and each wallet contains 12 dollars. Therefore, we calculate the total amount of money as follows: \[ 6 \text{ wallets} \times 12 \text{ dollars per wallet} = 72 \text{ dollars} \] ### Answer: 72 dollars
Expected answer: 72
Correct? Yes
Problem: A butterfly flaps its wings 9 times in one second. How many times does it flap its wings in 11 seconds?
GPT-4o:
To determine how many times the butterfly flaps its wings in 11 seconds, we need to multiply the number of flaps per second by the number of seconds. Given: - The butterfly flaps its wings 9 times in one second. - We need to find the number of flaps in 11 seconds. Calculation: \[ 9 \text{ flaps/second} \times 11 \text{ seconds} = 99 \text{ flaps} \] ### Answer: 99
Expected answer: 99
Correct? Yes
Problem: Now consider that the butterfly only flaps its wings 9 times in one second. How many times would it flap its wings in 4 seconds?
GPT-4o:
To determine how many times the butterfly flaps its wings in 4 seconds, we need to multiply the number of flaps per second by the number of seconds. Given: - The butterfly flaps its wings 9 times in one second. - We need to find the number of flaps in 4 seconds. Calculation: \[ 9 \text{ flaps/second} \times 4 \text{ seconds} = 36 \text{ flaps} \] ### Answer: 36
Expected answer: 36
Correct? Yes
Problem: A plane travels at a constant speed of 12 miles per minute. How many miles would the plane cover in 6 minutes?
GPT-4o:
To determine how many miles the plane would cover in 6 minutes, we can use the given constant speed and multiply it by the time traveled. The plane's speed is 12 miles per minute. Therefore, in 6 minutes, the distance covered would be: \[ \text{Distance} = \text{Speed} \times \text{Time} \] \[ \text{Distance} = 12 \, \text{miles/minute} \times 6 \, \text{minutes} \] \[ \text{Distance} = 72 \, \text{miles} \] ### Answer: 72 miles
Expected answer: 72
Correct? Yes
Problem: If the plane's speed was instead 11 miles per minute, how many miles would the plane cover in the same time period of 6 minutes?
GPT-4o:
To determine how many miles the plane would cover in 6 minutes at a speed of 11 miles per minute, we use the same method as before: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Given the speed is 11 miles per minute and the time is 6 minutes, we calculate: \[ \text{Distance} = 11 \, \text{miles/minute} \times 6 \, \text{minutes} \] \[ \text{Distance} = 66 \, \text{miles} \] ### Answer: 66 miles
Expected answer: 66
Correct? Yes
Problem: Josephine has 27 pairs of ice skates and wants to divide them equally among the 9 stores where she works. How many pairs of ice skates will each store receive?
GPT-4o:
To determine how many pairs of ice skates each store will receive, we need to divide the total number of pairs of ice skates by the number of stores. Josephine has 27 pairs of ice skates and there are 9 stores. We perform the division: \[ \frac{27}{9} = 3 \] So, each store will receive 3 pairs of ice skates. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: In a different scenario, Josephine originally had 9 pairs of ice skates instead of 27 that she wanted to distribute equally among the 9 stores. How many pairs of ice skates would each store receive in this case?
GPT-4o:
To determine how many pairs of ice skates each store will receive, we need to divide the total number of pairs of ice skates by the number of stores. Josephine has 9 pairs of ice skates and there are 9 stores. We perform the division: \[ \frac{9}{9} = 1 \] So, each store will receive 1 pair of ice skates. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: Each soap factory produces 7 bars of soap every hour. If a factory remains operational for 11 hours, how many bars of soap are produced?
GPT-4o:
To determine the total number of bars of soap produced, we need to multiply the number of bars produced per hour by the number of hours the factory operates. Given: - Each factory produces 7 bars of soap per hour. - The factory operates for 11 hours. Calculation: \[ 7 \text{ bars/hour} \times 11 \text{ hours} = 77 \text{ bars} \] ### Answer: 77
Expected answer: 77
Correct? Yes
Problem: Billy has 9 sets of kite with each set containing 3 kites. How many kites does he have in total?
GPT-4o:
To find the total number of kites Billy has, we need to multiply the number of sets by the number of kites in each set. Billy has 9 sets, and each set contains 3 kites. Therefore, we calculate: \[ 9 \text{ sets} \times 3 \text{ kites per set} = 27 \text{ kites} \] ### Answer: 27
Expected answer: 27
Correct? Yes
Problem: Billy decides to double his collection of kites. After doubling the initial amount, how many kites will he have in total?
GPT-4o:
Billy initially has 27 kites. If he decides to double his collection, we need to multiply the initial amount by 2. \[ 27 \text{ kites} \times 2 = 54 \text{ kites} \] ### Answer: 54
Expected answer: 54
Correct? Yes
Problem: Billy initially thought he had 9 sets of kites, but he actually had 11 sets. Given that each set contains 9 kites, how many kites does he really have in total?
GPT-4o:
To find the total number of kites Billy actually has, we need to multiply the number of sets by the number of kites in each set. Billy has 11 sets, and each set contains 9 kites. Therefore, we calculate: \[ 11 \text{ sets} \times 9 \text{ kites per set} = 99 \text{ kites} \] ### Answer: 99
Expected answer: 99
Correct? Yes
Problem: In a fairy tale, a magical creature multiplies a number by itself and gets an outcome. If the magical creature uses the number 4, what will be the outcome?
GPT-4o:
To find the outcome when the magical creature multiplies the number 4 by itself, we need to calculate \( 4 \times 4 \). \[ 4 \times 4 = 16 \] ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: Continuing the fairy tale, the magical creature took the outcome from her previous spell and multiplied it by 5. What is the new number after this spell?
GPT-4o:
The outcome from the previous spell was 16. Now, the magical creature multiplies this number by 5. \[ 16 \times 5 = 80 \] ### Answer: 80
Expected answer: 80
Correct? Yes
Problem: Continuing the magical story, suppose the magical creature had initially started with the number 11 instead of 4, and had multiplied this number by 4. What would have been the outcome of the first spell in that case?
GPT-4o:
To find the outcome when the magical creature multiplies the number 11 by 4, we need to calculate \( 11 \times 4 \). \[ 11 \times 4 = 44 \] ### Answer: 44
Expected answer: 44
Correct? Yes
Problem: There are 27 chairs and they need to be equally distributed among 3 rooms. How many chairs will each room have?
GPT-4o:
To determine how many chairs each room will have, we need to divide the total number of chairs by the number of rooms. Given: - Total number of chairs = 27 - Number of rooms = 3 We perform the division: \[ \frac{27}{3} = 9 \] So, each room will have 9 chairs. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: At first, there were 12 rooms instead of 3 to distribute the 27 chairs into. How many chairs would each room have in this case?
GPT-4o:
To determine how many chairs each room will have when there are 12 rooms, we need to divide the total number of chairs by the number of rooms. Given: - Total number of chairs = 27 - Number of rooms = 12 We perform the division: \[ \frac{27}{12} = 2.25 \] So, each room will have 2.25 chairs. ### Answer: 2.25
Expected answer: 9/4
Correct? Yes
Problem: A store stocks 56 toy cars uniformly over 8 shelves. How many toy cars are there per shelf?
GPT-4o:
To determine how many toy cars are on each shelf, we need to divide the total number of toy cars by the number of shelves. Given: - Total number of toy cars = 56 - Number of shelves = 8 We perform the division: \[ \frac{56}{8} = 7 \] So, there are 7 toy cars per shelf. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: Now, imagine if the store decided to stock only one toy car per shelf instead, distributing 8 toy cars uniformly over 8 shelves. How many toy cars would be there per shelf?
GPT-4o:
If the store decides to stock only one toy car per shelf and there are 8 toy cars to be distributed over 8 shelves, we can determine the number of toy cars per shelf by dividing the total number of toy cars by the number of shelves. Given: - Total number of toy cars = 8 - Number of shelves = 8 We perform the division: \[ \frac{8}{8} = 1 \] So, there would be 1 toy car per shelf. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: In a restaurant, every pizza slice takes 6 minutes to cook and a full pizza has 3 slices. If the restaurant wants to make 3 full pizzas, how long will it take in total?
GPT-4o:
First, let's determine the total number of slices in 3 full pizzas. Since each full pizza has 3 slices: \[ 3 \text{ pizzas} \times 3 \text{ slices per pizza} = 9 \text{ slices} \] Next, we know that each slice takes 6 minutes to cook. Therefore, the total cooking time for 9 slices is: \[ 9 \text{ slices} \times 6 \text{ minutes per slice} = 54 \text{ minutes} \] ### Answer: 54 minutes
Expected answer: 54
Correct? Yes
Problem: In addition to the 3 pizzas, the restaurant also wants to make a special pizza that takes the same amount of time as the 3 pizzas combined. How long will it take to make the special pizza?
GPT-4o:
We previously calculated that making 3 full pizzas takes 54 minutes. Since the special pizza takes the same amount of time as the 3 pizzas combined, it will also take: ### Answer: 54 minutes
Expected answer: 54
Correct? Yes
Problem: The restaurant has revised its pizza cooking time. Now, each slice of pizza takes only 1 minute to cook but a full pizza still has 3 slices. Now, how long will it take to make 3 full pizzas?
GPT-4o:
First, let's determine the total number of slices in 3 full pizzas. Since each full pizza has 3 slices: \[ 3 \text{ pizzas} \times 3 \text{ slices per pizza} = 9 \text{ slices} \] Next, we know that each slice now takes only 1 minute to cook. Therefore, the total cooking time for 9 slices is: \[ 9 \text{ slices} \times 1 \text{ minute per slice} = 9 \text{ minutes} \] ### Answer: 9 minutes
Expected answer: 9
Correct? Yes
Problem: Arthur drives his car 7 hours each day for 4 days. How many total hours did Arthur spend driving his car over this period?
GPT-4o:
To find the total number of hours Arthur spent driving his car over the 4 days, we need to multiply the number of hours he drives each day by the number of days. Arthur drives 7 hours each day for 4 days: \[ 7 \text{ hours/day} \times 4 \text{ days} = 28 \text{ hours} \] ### Answer: 28 hours.
Expected answer: 28
Correct? Yes
Problem: Considering the previous problem, what if Arthur only drove his car for 2 hours each day for that same 4-day period? How many total hours did Arthur spend driving his car over this period?
GPT-4o:
To find the total number of hours Arthur spent driving his car over the 4 days when he drives 2 hours each day, we need to multiply the number of hours he drives each day by the number of days. Arthur drives 2 hours each day for 4 days: \[ 2 \text{ hours/day} \times 4 \text{ days} = 8 \text{ hours} \] ### Answer: 8 hours.
Expected answer: 8
Correct? Yes
Problem: If each blanket requires 6 yards of yarn for one section, and each finished blanket is made up of 5 such sections, how many yards of yarn do you need to create one blanket?
GPT-4o:
To determine the total amount of yarn needed for one blanket, we need to calculate the total yards of yarn required for all sections of the blanket. Each section requires 6 yards of yarn, and there are 5 sections in one blanket. Therefore, the total amount of yarn needed is: \[ 6 \text{ yards/section} \times 5 \text{ sections} = 30 \text{ yards} \] ### Answer: 30 yards
Expected answer: 30
Correct? Yes
Problem: Following the previous problem, if you were given the task to make two blankets with the same size and design, how many yards of yarn would you need in total?
GPT-4o:
To determine the total amount of yarn needed for two blankets, we need to calculate the total yards of yarn required for one blanket and then multiply by the number of blankets. From the previous problem, we know that one blanket requires 30 yards of yarn. Therefore, for two blankets, the total amount of yarn needed is: \[ 30 \text{ yards/blanket} \times 2 \text{ blankets} = 60 \text{ yards} \] ### Answer: 60 yards
Expected answer: 60
Correct? Yes
Problem: Following the initial problem, consider if each blanket requires six yards of yarn for just one section, but the new design demands that a blanket is made up of 12 such sections. How many yards of yarn would you now need to create one blanket with this new design?
GPT-4o:
To determine the total amount of yarn needed for one blanket with the new design, we need to calculate the total yards of yarn required for all sections of the blanket. Each section requires 6 yards of yarn, and there are now 12 sections in one blanket. Therefore, the total amount of yarn needed is: \[ 6 \text{ yards/section} \times 12 \text{ sections} = 72 \text{ yards} \] ### Answer: 72 yards
Expected answer: 72
Correct? Yes
Problem: A bus travels at a speed of 7 miles per hour. How many miles will the bus travel after 6 hours?
GPT-4o:
To determine how many miles the bus will travel after 6 hours, we can use the formula for distance, which is: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Given: - Speed = 7 miles per hour - Time = 6 hours Substitute the given values into the formula: \[ \text{Distance} = 7 \, \text{miles/hour} \times 6 \, \text{hours} \] \[ \text{Distance} = 42 \, \text{miles} \] ### Answer: 42 miles
Expected answer: 42
Correct? Yes
Problem: Following the previous scenario, consider that the bus was actually traveling at a speed of 10 miles per hour, not 7. How many miles would the bus have travelled after 6 hours in this case?
GPT-4o:
To determine how many miles the bus will travel after 6 hours at a speed of 10 miles per hour, we use the same distance formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Given: - Speed = 10 miles per hour - Time = 6 hours Substitute the given values into the formula: \[ \text{Distance} = 10 \, \text{miles/hour} \times 6 \, \text{hours} \] \[ \text{Distance} = 60 \, \text{miles} \] ### Answer: 60 miles
Expected answer: 60
Correct? Yes
Problem: Superhero Starlight has a power level that is the product of multiplying 3 by 5. What is Starlight's power level?
GPT-4o:
To find Starlight's power level, we need to multiply 3 by 5. \[ 3 \times 5 = 15 \] ### Answer: 15
Expected answer: 15
Correct? Yes
Problem: Superhero Starlight, after completing her special power-up training, can now increase her initial power level by three times. If her initial power level was the product of multiplying 3 by 5, what is her new power level after the power-up training?
GPT-4o:
First, we need to determine Starlight's initial power level by multiplying 3 by 5: \[ 3 \times 5 = 15 \] Next, we need to calculate her new power level after increasing it by three times. This means we multiply her initial power level by 3: \[ 15 \times 3 = 45 \] ### Answer: 45
Expected answer: 45
Correct? Yes
Problem: Considering that Superhero Starlight initially had a power level that was the product of multiplying 3 by 5, let's imagine if her initial power level was actually the product of multiplying 3 by 6. What would her initial power level be in this scenario?
GPT-4o:
To find Starlight's initial power level in this new scenario, we need to multiply 3 by 6. \[ 3 \times 6 = 18 \] ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: Jessica has a backpack that when you measure one side, is 10 inches long. What is the area of one side of Jessica's backpack assuming it is a perfect square?
GPT-4o:
To find the area of one side of Jessica's backpack, we need to use the formula for the area of a square, which is: \[ \text{Area} = \text{side length} \times \text{side length} \] Given that one side of the backpack is 10 inches long, we can substitute this value into the formula: \[ \text{Area} = 10 \, \text{inches} \times 10 \, \text{inches} \] \[ \text{Area} = 100 \, \text{square inches} \] ### Answer: 100 square inches
Expected answer: 100
Correct? Yes
Problem: Now consider that Jessica has another backpack, this one has a side that measures 4 inches. What is the area of one side of this backpack, again assuming it is a perfect square?
GPT-4o:
To find the area of one side of Jessica's second backpack, we use the formula for the area of a square: \[ \text{Area} = \text{side length} \times \text{side length} \] Given that one side of the backpack is 4 inches long, we substitute this value into the formula: \[ \text{Area} = 4 \, \text{inches} \times 4 \, \text{inches} \] \[ \text{Area} = 16 \, \text{square inches} \] ### Answer: 16 square inches
Expected answer: 16
Correct? Yes
Problem: Captain Sparrow found 36 gold doubloons. He wants to divide it equally among his 3 crew members. How many gold doubloons will each crew member get?
GPT-4o:
To determine how many gold doubloons each crew member will get, we need to divide the total number of gold doubloons by the number of crew members. The total number of gold doubloons is 36, and there are 3 crew members. We perform the division: \[ \frac{36}{3} = 12 \] So, each crew member will get 12 gold doubloons. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: Suppose Captain Sparrow had initially found 36 gold doubloons, but this time he wants to divide them equally among 7 crew members, not 3. How many gold doubloons will each crew member get now?
GPT-4o:
To determine how many gold doubloons each crew member will get, we need to divide the total number of gold doubloons by the number of crew members. The total number of gold doubloons is 36, and there are 7 crew members. We perform the division: \[ \frac{36}{7} \approx 5.14 \] Since we are dealing with gold doubloons, which are typically whole units, each crew member will get 5 gold doubloons, and there will be a remainder. To find the remainder: \[ 36 \div 7 = 5 \text{ remainder } 1 \] So, each crew member will get 5 gold doubloons, and there will be 1 gold doubloon left over. ### Answer: 5 gold doubloons each, with 1 gold doubloon left over.
Expected answer: 36/7
Correct? No
Problem: A robot factory produces 5 robots each hour. If the factory increases its output to twice this amount, how many robots will it produce each hour?
GPT-4o:
First, we need to determine the current output of the factory, which is 5 robots each hour. Next, we need to find out what twice this amount would be. To do this, we multiply the current output by 2: \[ 5 \text{ robots/hour} \times 2 = 10 \text{ robots/hour} \] Therefore, if the factory increases its output to twice the current amount, it will produce 10 robots each hour. ### Answer: 10 robots/hour
Expected answer: 10
Correct? Yes
Problem: In the previous problem, the robot factory increased its output to twice its original amount, making 10 robots each hour. If the factory were to then multiply this new hourly output by the same amount they were originally making each hour (5 robots), how many robots would the factory make every hour?
GPT-4o:
We know from the previous problem that the factory's new output is 10 robots each hour. Now, we need to multiply this new output by the original hourly output, which is 5 robots each hour: \[ 10 \text{ robots/hour} \times 5 = 50 \text{ robots/hour} \] Therefore, if the factory multiplies its new hourly output by the original hourly output, it will make 50 robots every hour. ### Answer: 50 robots/hour
Expected answer: 50
Correct? Yes
Problem: In the previous problem, the robot factory was originally making 5 robots each hour. However, if the factory were to increase its output to six times the original amount instead, how many robots would it produce each hour?
GPT-4o:
First, we need to determine the current output of the factory, which is 5 robots each hour. Next, we need to find out what six times this amount would be. To do this, we multiply the current output by 6: \[ 5 \text{ robots/hour} \times 6 = 30 \text{ robots/hour} \] Therefore, if the factory increases its output to six times the original amount, it will produce 30 robots each hour. ### Answer: 30 robots/hour
Expected answer: 30
Correct? Yes
Problem: If one bike wheel has a radius of 81 / 9 units, and the height of a certain signpost is 9 times this radius, what is the height of the signpost?
GPT-4o:
First, we need to determine the radius of the bike wheel. The radius is given as \( \frac{81}{9} \) units. \[ \frac{81}{9} = 9 \text{ units} \] Next, we need to find the height of the signpost, which is 9 times the radius of the bike wheel. \[ 9 \times 9 = 81 \text{ units} \] ### Answer: 81 units
Expected answer: 81
Correct? Yes
Problem: If one bike wheel still has a radius of 81/9 units, but now the height of a certain bike rack is only 6 times this radius, what is the height of the bike rack?
GPT-4o:
First, we need to determine the radius of the bike wheel. The radius is given as \( \frac{81}{9} \) units. \[ \frac{81}{9} = 9 \text{ units} \] Next, we need to find the height of the bike rack, which is 6 times the radius of the bike wheel. \[ 6 \times 9 = 54 \text{ units} \] ### Answer: 54 units
Expected answer: 54
Correct? Yes
Problem: On a sunny day, Jamie took some time to swing on a tree. He swung 11 times in every minute and he spent 1 minute swinging. How many times did Jamie swing in total?
GPT-4o:
To determine the total number of times Jamie swung on the tree, we need to multiply the number of swings per minute by the number of minutes he spent swinging. Jamie swung 11 times per minute and he spent 1 minute swinging. Total swings = (number of swings per minute) Γ (number of minutes) Total swings = 11 swings/minute Γ 1 minute ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: Following on from the previous problem, if Jamie continued swinging at the same pace for 3 more minutes, how many times would he have swung in total over those extra minutes?
GPT-4o:
To determine the total number of swings Jamie made in the additional 3 minutes, we need to multiply the number of swings per minute by the number of additional minutes. Jamie swings 11 times per minute. For 3 additional minutes: Total swings in 3 minutes = (number of swings per minute) Γ (number of additional minutes) Total swings in 3 minutes = 11 swings/minute Γ 3 minutes Total swings in 3 minutes = 33 swings ### Answer: 33
Expected answer: 33
Correct? Yes
Problem: After his first session, Jamie took a break and then returned to the swing. This second time, he swung 6 times per minute for one minute. How many times did he swing in that minute?
GPT-4o:
To determine the number of times Jamie swung during his second session, we need to multiply the number of swings per minute by the number of minutes he spent swinging. Jamie swung 6 times per minute and he spent 1 minute swinging. Total swings = (number of swings per minute) Γ (number of minutes) Total swings = 6 swings/minute Γ 1 minute ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: James has 9 robot toys and he buys the same amount again. How many robot toys does he have now?
GPT-4o:
To determine how many robot toys James has now, we need to add the number of robot toys he originally had to the number he bought. James originally has 9 robot toys. He buys the same amount again, which means he buys 9 more robot toys. Now, we add the original number of robot toys to the number he bought: \[ 9 + 9 = 18 \] ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: Let's say instead of initially having 9 robot toys and buying the same amount again, James originally had 9 robot toys, but this time, he decided to buy 5 more sets of 9 toys each. How many robot toys does James have now?
GPT-4o:
To determine how many robot toys James has now, we need to calculate the total number of robot toys he has after buying 5 more sets of 9 toys each. First, let's calculate the number of robot toys in the 5 sets: \[ 5 \times 9 = 45 \] Next, we add this to the number of robot toys James originally had: \[ 9 + 45 = 54 \] ### Answer: 54
Expected answer: 54
Correct? Yes
Problem: A farmer has 11 chickens and each chicken lays 7 eggs in a week. How many eggs do the chickens lay in total in a week?
GPT-4o:
To determine the total number of eggs laid by the chickens in a week, we need to multiply the number of chickens by the number of eggs each chicken lays in a week. Given: - Number of chickens = 11 - Number of eggs each chicken lays in a week = 7 We calculate the total number of eggs as follows: \[ \text{Total eggs} = \text{Number of chickens} \times \text{Number of eggs per chicken} \] \[ \text{Total eggs} = 11 \times 7 \] \[ \text{Total eggs} = 77 \] ### Answer: 77
Expected answer: 77
Correct? Yes
Problem: The farmer from the previous problem sells each egg for 1 dollar. How much money does the farmer make in a week by selling all the eggs?
GPT-4o:
To determine how much money the farmer makes in a week by selling all the eggs, we need to multiply the total number of eggs by the price per egg. From the previous problem, we know: - Total number of eggs laid in a week = 77 - Price per egg = 1 dollar We calculate the total money earned as follows: \[ \text{Total money earned} = \text{Total number of eggs} \times \text{Price per egg} \] \[ \text{Total money earned} = 77 \times 1 \] \[ \text{Total money earned} = 77 \] ### Answer: 77 dollars
Expected answer: 77
Correct? Yes
Problem: In the previous problem, if the farmer only had 2 chickens instead of 11, and each chicken still lays 7 eggs in a week, how many eggs would the chickens lay in total in a week?
GPT-4o:
To determine the total number of eggs laid by the 2 chickens in a week, we need to multiply the number of chickens by the number of eggs each chicken lays in a week. Given: - Number of chickens = 2 - Number of eggs each chicken lays in a week = 7 We calculate the total number of eggs as follows: \[ \text{Total eggs} = \text{Number of chickens} \times \text{Number of eggs per chicken} \] \[ \text{Total eggs} = 2 \times 7 \] \[ \text{Total eggs} = 14 \] ### Answer: 14
Expected answer: 14
Correct? Yes
Problem: In an enchanting forest, a certain type of tree grows 4 centimeters each day. If it only grows half of this amount each night, how many centimeters does the tree grow overnight?
GPT-4o:
To determine how many centimeters the tree grows overnight, we need to calculate half of the amount it grows each day. The tree grows 4 centimeters each day. Therefore, the amount it grows overnight is: \[ \frac{4 \text{ cm}}{2} = 2 \text{ cm} \] ### Answer: 2 cm
Expected answer: 2
Correct? Yes
Problem: The enchanted tree that has been growing in the forest doesn't stop there. Overnight, it grows half of its daily growth rate, which is 4 cm. If this overnight height is multiplied by 10, how long is the final growth of the tree over these 10 nights?
GPT-4o:
First, we need to determine the overnight growth of the tree. As previously calculated, the tree grows 2 centimeters overnight. Next, we need to find the total growth over 10 nights. Since the tree grows 2 centimeters each night, we multiply this growth by 10: \[ 2 \text{ cm/night} \times 10 \text{ nights} = 20 \text{ cm} \] ### Answer: 20 cm
Expected answer: 20
Correct? Yes
Problem: The enchanted tree that was previously growing at an overnight rate of 4 cm changes its growth pattern. Now, it starts to grow at a rate of 10 centimeters each day, but it still grows only half of this amount each night. How many centimeters does the tree now grow overnight?
GPT-4o:
To determine how many centimeters the tree now grows overnight, we need to calculate half of the new daily growth rate. The tree now grows 10 centimeters each day. Therefore, the amount it grows overnight is: \[ \frac{10 \text{ cm}}{2} = 5 \text{ cm} \] ### Answer: 5 cm
Expected answer: 5
Correct? Yes
Problem: In a laboratory experiment, a group of 77 mice are divided equally among 11 cages. How many mice would be in each cage?
GPT-4o:
To determine how many mice are in each cage, we need to divide the total number of mice by the number of cages. Given: - Total number of mice = 77 - Number of cages = 11 We perform the division: \[ \frac{77}{11} = 7 \] So, there are 7 mice in each cage. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: After having divided the mice among the 11 cages, the scientist realized that she made a mistake and originally there were only 77 mice but some of them were counted twice. After correcting for this mistake, she realized that she actually only had 77 / 2 mice. How many mice did the scientist have originally?
GPT-4o:
To find out how many mice the scientist originally had, we need to correct the count by dividing the initial number of mice by 2. Given: - Initial (incorrect) count of mice = 77 - Corrected count = \( \frac{77}{2} \) Perform the division: \[ \frac{77}{2} = 38.5 \] Since the number of mice must be a whole number, it seems there was an error in the problem statement. However, if we assume the problem allows for fractional mice, the corrected count would be 38.5. ### Answer: 38.5
Expected answer: 77/2
Correct? Yes
Problem: Sally makes earrings. She needs 35 beads to make a set of earrings, but she divides this amount by 5 to make each individual earring. If she wants to make 8 earrings, how many beads will she need in total?
GPT-4o:
First, we need to determine how many beads are required to make one earring. According to the problem, Sally divides the total number of beads for a set of earrings (35 beads) by 5 to get the number of beads per individual earring. \[ \text{Beads per earring} = \frac{35}{5} = 7 \] Next, we need to find out how many beads are required to make 8 earrings. We do this by multiplying the number of beads per earring by the number of earrings Sally wants to make. \[ \text{Total beads needed} = 7 \times 8 = 56 \] ### Answer: 56
Expected answer: 56
Correct? Yes
Problem: Sally realizes that she made a mistake in her calculations for making earrings. Instead of needing 35 beads for a set of earrings, she only needs 35 beads for a display of five earrings. Therefore, she recalculates and finds that to make each earring she only needs to divide this new amount by five. If she wants to make just 2 earrings, how many beads will she need now?
GPT-4o:
First, we need to determine how many beads are required to make one earring based on the new information. Sally needs 35 beads for a display of five earrings. To find the number of beads per individual earring, we divide the total number of beads by the number of earrings in the display. \[ \text{Beads per earring} = \frac{35}{5} = 7 \] Next, we need to find out how many beads are required to make 2 earrings. We do this by multiplying the number of beads per earring by the number of earrings Sally wants to make. \[ \text{Total beads needed} = 7 \times 2 = 14 \] ### Answer: 14
Expected answer: 14
Correct? Yes
Problem: Brenda has 9 apples and wishes to divide them equally amongst her 9 friends, so each friend receives the same amount. How many apples will each friend get?
GPT-4o:
To determine how many apples each friend will receive, we need to divide the total number of apples by the number of friends. Brenda has 9 apples and 9 friends. We perform the division: \[ \frac{9 \text{ apples}}{9 \text{ friends}} = 1 \text{ apple per friend} \] So, each friend will receive 1 apple. ### Answer: 1 apple per friend.
Expected answer: 1
Correct? Yes
Problem: In a new scenario, Brenda has 9 apples but this time she only wants to divide them evenly among her 2 closest friends. Given this change, how many apples will each friend receive now?
GPT-4o:
To determine how many apples each of Brenda's 2 closest friends will receive, we need to divide the total number of apples by the number of friends. Brenda has 9 apples and 2 friends. We perform the division: \[ \frac{9 \text{ apples}}{2 \text{ friends}} = 4.5 \text{ apples per friend} \] So, each friend will receive 4.5 apples. ### Answer: 4.5 apples per friend.
Expected answer: 9/2
Correct? No
Problem: In a circus, a tightrope is set 10 feet off the ground. A stuntman wants to do a daring stunt - he wants to walk from one side of the tightrope to the other. The tightrope is five times the height above the ground. What distance will he need to walk to complete his stunt?
GPT-4o:
To determine the distance the stuntman needs to walk, we need to find the length of the tightrope. The problem states that the tightrope is set 10 feet off the ground and that the length of the tightrope is five times this height. First, we calculate the length of the tightrope: \[ \text{Length of the tightrope} = 5 \times \text{height above the ground} \] \[ \text{Length of the tightrope} = 5 \times 10 \text{ feet} \] \[ \text{Length of the tightrope} = 50 \text{ feet} \] Therefore, the stuntman will need to walk 50 feet to complete his stunt. ### Answer: 50 feet
Expected answer: 50
Correct? Yes
Problem: After completing his daring stunt, the tightrope walker decides to challenge himself further and wants to perform the same stunt on a tightrope that's only 1 foot off the ground. Now, how far would he need to walk considering the tightrope is still five times the height above the ground?
GPT-4o:
To determine the distance the stuntman needs to walk on the new tightrope, we need to find the length of the tightrope when it is set 1 foot off the ground. The problem states that the length of the tightrope is five times the height above the ground. First, we calculate the length of the tightrope: \[ \text{Length of the tightrope} = 5 \times \text{height above the ground} \] \[ \text{Length of the tightrope} = 5 \times 1 \text{ foot} \] \[ \text{Length of the tightrope} = 5 \text{ feet} \] Therefore, the stuntman will need to walk 5 feet to complete his stunt on the new tightrope. ### Answer: 5 feet
Expected answer: 5
Correct? Yes
Problem: The length of one side of a square is equal to the result of dividing 30 by 6. What is the total area of the square?
GPT-4o:
First, we need to determine the length of one side of the square. The length of one side is given by dividing 30 by 6: \[ \text{Side length} = \frac{30}{6} = 5 \] Next, we calculate the area of the square. The area \( A \) of a square is given by the formula: \[ A = \text{side length}^2 \] Substituting the side length we found: \[ A = 5^2 = 25 \] ### Answer: 25
Expected answer: 25
Correct? Yes
Problem: The length of one side of a square is equal to the result of dividing 30 by 6. The total area of the square is found by multiplying the length of one side by itself. Now, if we multiply this area by 3, what will be the new value?
GPT-4o:
First, we determine the length of one side of the square by dividing 30 by 6: \[ \text{Side length} = \frac{30}{6} = 5 \] Next, we calculate the area of the square. The area \( A \) of a square is given by the formula: \[ A = \text{side length}^2 \] Substituting the side length we found: \[ A = 5^2 = 25 \] Now, we need to multiply this area by 3: \[ \text{New value} = 25 \times 3 = 75 \] ### Answer: 75
Expected answer: 75
Correct? Yes
Problem: In the original problem, the length of one side of the square was found by dividing 30 by 6. Now consider a new scenario where the length of the square is instead found by dividing number 12 by 6. What would be the total area of this new square?
GPT-4o:
First, we need to determine the length of one side of the new square. The length of one side is given by dividing 12 by 6: \[ \text{Side length} = \frac{12}{6} = 2 \] Next, we calculate the area of the new square. The area \( A \) of a square is given by the formula: \[ A = \text{side length}^2 \] Substituting the side length we found: \[ A = 2^2 = 4 \] ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: A certain star emits 7 particles every second. If this continues for 8 seconds, how many particles does the star emit in total?
GPT-4o:
To determine the total number of particles emitted by the star, we need to multiply the rate of emission by the duration of time. The star emits 7 particles every second. If this continues for 8 seconds, we calculate the total number of particles as follows: \[ 7 \, \text{particles/second} \times 8 \, \text{seconds} = 56 \, \text{particles} \] ### Answer: 56
Expected answer: 56
Correct? Yes
Problem: If the first star, instead of emitting particles for 8 seconds, only emits particles for 5 seconds, how many particles will then it emit?
GPT-4o:
To determine the total number of particles emitted by the star over 5 seconds, we use the same method of multiplying the rate of emission by the duration of time. The star emits 7 particles every second. If this continues for 5 seconds, we calculate the total number of particles as follows: \[ 7 \, \text{particles/second} \times 5 \, \text{seconds} = 35 \, \text{particles} \] ### Answer: 35
Expected answer: 35
Correct? Yes
Problem: A shoe factory can create 24 shoes in three hours. If the factory runs for five hours, how many shoes will be produced?
GPT-4o:
To determine how many shoes the factory can produce in five hours, we first need to find the rate at which the factory produces shoes per hour. The factory produces 24 shoes in 3 hours. Therefore, the production rate per hour is: \[ \text{Production rate} = \frac{24 \text{ shoes}}{3 \text{ hours}} = 8 \text{ shoes per hour} \] Next, we calculate the total number of shoes produced in five hours by multiplying the production rate by the number of hours: \[ \text{Total shoes} = 8 \text{ shoes per hour} \times 5 \text{ hours} = 40 \text{ shoes} \] ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: The shoe factory increased its production time from five hours to ten hours. Now, how many shoes will the factory produce if it's still able to create 24 shoes every three hours?
GPT-4o:
To determine how many shoes the factory will produce in ten hours, we first need to find the rate at which the factory produces shoes per hour. The factory produces 24 shoes in 3 hours. Therefore, the production rate per hour is: \[ \text{Production rate} = \frac{24 \text{ shoes}}{3 \text{ hours}} = 8 \text{ shoes per hour} \] Next, we calculate the total number of shoes produced in ten hours by multiplying the production rate by the number of hours: \[ \text{Total shoes} = 8 \text{ shoes per hour} \times 10 \text{ hours} = 80 \text{ shoes} \] ### Answer: 80
Expected answer: 80
Correct? Yes
Problem: A unique species of butterfly only lives for 5 days in each month. Considering this fact, how many days total does the butterfly species live in a span of a year, which is 12 months?
GPT-4o:
To determine the total number of days the butterfly species lives in a year, we need to consider the lifespan of the butterfly in each month and then multiply by the number of months in a year. Given: - The butterfly lives for 5 days each month. - There are 12 months in a year. First, calculate the total number of days the butterfly lives in one year: \[ 5 \text{ days/month} \times 12 \text{ months/year} = 60 \text{ days/year} \] ### Answer: 60 days
Expected answer: 60
Correct? Yes
Problem: Considering the same unique species of butterfly, but now in a different region it only lives for 5 days each week instead of per month. How many days total does the butterfly species live in a 7-week span?
GPT-4o:
To determine the total number of days the butterfly species lives in a 7-week span, we need to consider the lifespan of the butterfly in each week and then multiply by the number of weeks. Given: - The butterfly lives for 5 days each week. - We are considering a span of 7 weeks. First, calculate the total number of days the butterfly lives in 7 weeks: \[ 5 \text{ days/week} \times 7 \text{ weeks} = 35 \text{ days} \] ### Answer: 35 days
Expected answer: 35
Correct? Yes
Problem: In fairy land, one ordinary mushroom provides food for 10 fairies for a day. If a magic mushroom can provide food as 4 ordinary mushrooms, how many fairies can a magic mushroom feed for a day?
GPT-4o:
First, we need to determine how many fairies one magic mushroom can feed. We know that: - One ordinary mushroom provides food for 10 fairies for a day. - One magic mushroom is equivalent to 4 ordinary mushrooms. Therefore, the number of fairies that one magic mushroom can feed is: \[ 4 \text{ ordinary mushrooms} \times 10 \text{ fairies per ordinary mushroom} = 40 \text{ fairies} \] ### Answer: 40 fairies
Expected answer: 40
Correct? Yes
Problem: In fairy land, change the original number of fairies an ordinary mushroom can feed from 10 to 11. With this change, how many fairies can a magic mushroom, which can provide food as 4 ordinary mushrooms, feed for a day?
GPT-4o:
First, we need to determine how many fairies one magic mushroom can feed with the updated information. We know that: - One ordinary mushroom now provides food for 11 fairies for a day. - One magic mushroom is equivalent to 4 ordinary mushrooms. Therefore, the number of fairies that one magic mushroom can feed is: \[ 4 \text{ ordinary mushrooms} \times 11 \text{ fairies per ordinary mushroom} = 44 \text{ fairies} \] ### Answer: 44 fairies
Expected answer: 44
Correct? Yes
Problem: A river is flowing at a rate of 4 kilometers per hour. How far can the river flow in 10 hours?
GPT-4o:
To determine how far the river can flow in 10 hours, we need to use the formula for distance, which is: \[ \text{Distance} = \text{Rate} \times \text{Time} \] Given: - Rate of the river = 4 kilometers per hour - Time = 10 hours Substitute the given values into the formula: \[ \text{Distance} = 4 \, \text{km/hr} \times 10 \, \text{hr} \] \[ \text{Distance} = 40 \, \text{km} \] ### Answer: 40 km
Expected answer: 40
Correct? Yes
Problem: If the speed of the river were instead 4 kilometers per hour for 2 hours, how far would the river flow within these 2 hours?
GPT-4o:
To determine how far the river can flow in 2 hours at a speed of 4 kilometers per hour, we use the same distance formula: \[ \text{Distance} = \text{Rate} \times \text{Time} \] Given: - Rate of the river = 4 kilometers per hour - Time = 2 hours Substitute the given values into the formula: \[ \text{Distance} = 4 \, \text{km/hr} \times 2 \, \text{hr} \] \[ \text{Distance} = 8 \, \text{km} \] ### Answer: 8 km
Expected answer: 8
Correct? Yes
Problem: A slide is double the height of Ava who is 12 feet tall. How tall is the slide?
GPT-4o:
To determine the height of the slide, we need to double Ava's height. Ava is 12 feet tall. So, the height of the slide is: \[ 2 \times 12 = 24 \] ### Answer: 24 feet
Expected answer: 24
Correct? Yes
Problem: Following up on the last problem: If Ava decides to triple the height of the slide that is double her height, how high will the new slide be?
GPT-4o:
First, we know from the previous problem that the height of the slide is 24 feet. To find the height of the new slide, we need to triple the height of the current slide: \[ 3 \times 24 = 72 \] ### Answer: 72 feet
Expected answer: 72
Correct? Yes
Problem: In the previous problem, Ava was initially considering a slide double her height when she was 12 feet tall. However, let's say Ava is actually 11 feet tall. In that case, how high would the slide be if it was still double her height?
GPT-4o:
To determine the height of the slide when Ava is 11 feet tall, we need to double her current height. So, the height of the slide is: \[ 2 \times 11 = 22 \] ### Answer: 22 feet
Expected answer: 22
Correct? Yes
Problem: There's a tap which fills a tank at a rate of 2 liters per minute. How much water will be in the tank after 9 minutes?
GPT-4o:
To determine how much water will be in the tank after 9 minutes, we need to multiply the rate at which the tap fills the tank by the amount of time the tap is running. The rate at which the tap fills the tank is 2 liters per minute. The time the tap is running is 9 minutes. So, we calculate: \[ 2 \text{ liters/minute} \times 9 \text{ minutes} = 18 \text{ liters} \] ### Answer: 18 liters
Expected answer: 18
Correct? Yes
Problem: What if the tap was turned on for 7 minutes instead of 9 minutes? How much water would the tap fill in the tank in that case?
GPT-4o:
To determine how much water will be in the tank after 7 minutes, we need to multiply the rate at which the tap fills the tank by the amount of time the tap is running. The rate at which the tap fills the tank is 2 liters per minute. The time the tap is running is 7 minutes. So, we calculate: \[ 2 \text{ liters/minute} \times 7 \text{ minutes} = 14 \text{ liters} \] ### Answer: 14 liters
Expected answer: 14
Correct? Yes
Problem: Fred received 12 letters in one week and he reads them evenly over 3 days. How many letters does he read per day?
GPT-4o:
To determine how many letters Fred reads per day, we need to divide the total number of letters by the number of days. Fred received 12 letters in one week and reads them evenly over 3 days. We perform the division: \[ \frac{12 \text{ letters}}{3 \text{ days}} = 4 \text{ letters per day} \] ### Answer: 4 letters per day.
Expected answer: 4
Correct? Yes
Problem: Fred received 11 letters in one week instead of 12. If he still reads them evenly over 3 days, how many letters does he read per day now?
GPT-4o:
To determine how many letters Fred reads per day, we need to divide the total number of letters by the number of days. Fred received 11 letters in one week and reads them evenly over 3 days. We perform the division: \[ \frac{11 \text{ letters}}{3 \text{ days}} = \frac{11}{3} \approx 3.67 \text{ letters per day} \] ### Answer: 3.67 letters per day.
Expected answer: 11/3
Correct? No
Problem: A toy car factory produces 8 cars every hour 24/7. If the factory runs for 12 hours a day, how many cars will it produce in one day?
GPT-4o:
To determine how many toy cars the factory produces in one day, we need to consider the production rate and the number of hours the factory operates each day. The factory produces 8 cars every hour. If it runs for 12 hours a day, we can calculate the total number of cars produced in one day by multiplying the production rate by the number of hours: \[ \text{Number of cars produced in one day} = \text{Production rate per hour} \times \text{Number of hours per day} \] \[ \text{Number of cars produced in one day} = 8 \, \text{cars/hour} \times 12 \, \text{hours/day} \] \[ \text{Number of cars produced in one day} = 96 \, \text{cars} \] ### Answer: 96
Expected answer: 96
Correct? Yes
Problem: After the shifts mentioned in the previous problem, the toy car factory decides to change its production rate. Now, instead of producing 8 cars per hour as before, it produces 5 cars per hour. If the factory continues to run for 12 hours a day, how many cars will it produce in one day now?
GPT-4o:
To determine the new number of toy cars produced in one day after the change in production rate, we need to use the new production rate and the number of hours the factory operates each day. The new production rate is 5 cars per hour. The factory continues to run for 12 hours a day. We can calculate the total number of cars produced in one day by multiplying the new production rate by the number of hours: \[ \text{Number of cars produced in one day} = \text{New production rate per hour} \times \text{Number of hours per day} \] \[ \text{Number of cars produced in one day} = 5 \, \text{cars/hour} \times 12 \, \text{hours/day} \] \[ \text{Number of cars produced in one day} = 60 \, \text{cars} \] ### Answer: 60
Expected answer: 60
Correct? Yes
Problem: If baby Lily got 44 toys divided evenly among her 4 cousins, each cousin would get 'i' number of toys. If we multiply 'i' by 5, how many toys would that represent?
GPT-4o:
First, we need to determine how many toys each cousin would get if 44 toys are divided evenly among 4 cousins. This can be calculated as follows: \[ i = \frac{44}{4} \] \[ i = 11 \] Each cousin would get 11 toys. Next, we need to find the result of multiplying 'i' by 5: \[ 11 \times 5 = 55 \] ### Answer: 55
Expected answer: 55
Correct? Yes
Problem: If instead Baby Lily originally got 44 toys but this time, she divided them evenly among her 11 friends, each friend would get 'i' number of toys. If we multiply 'i' by 5, how many toys would that represent?
GPT-4o:
First, we need to determine how many toys each friend would get if 44 toys are divided evenly among 11 friends. This can be calculated as follows: \[ i = \frac{44}{11} \] \[ i = 4 \] Each friend would get 4 toys. Next, we need to find the result of multiplying 'i' by 5: \[ 4 \times 5 = 20 \] ### Answer: 20
Expected answer: 20
Correct? Yes
Problem: Mike has $9 and he wants to divide it equally among his 3 children. How much money will each child recieve?
GPT-4o:
To determine how much money each child will receive, we need to divide the total amount of money by the number of children. Mike has $9 and he wants to divide it equally among his 3 children. We perform the division: \[ \frac{9}{3} = 3 \] So, each child will receive $3. ### Answer: $3
Expected answer: 3
Correct? Yes
Problem: If each of Mike's children decided to save the money they received from their father every month for a year, how much money would each child have saved by the end of the year?
GPT-4o:
Each of Mike's children receives $3 every month. To find out how much money each child will have saved by the end of the year, we need to multiply the monthly amount by the number of months in a year. There are 12 months in a year. Therefore, we calculate: \[ 3 \text{ dollars/month} \times 12 \text{ months} = 36 \text{ dollars} \] So, each child will have saved $36 by the end of the year. ### Answer: $36
Expected answer: 36
Correct? Yes
Problem: If Mike had $11 instead of $9 and he still decided to divide it equally among his 3 children, how much money would each child receive now?
GPT-4o:
To determine how much money each child will receive, we need to divide the total amount of money by the number of children. Mike has $11 and he wants to divide it equally among his 3 children. We perform the division: \[ \frac{11}{3} \approx 3.67 \] So, each child will receive approximately $3.67. ### Answer: $3.67
Expected answer: 11/3
Correct? No
Problem: If a cow produces 72 liters of milk in 12 days, and you need to find out how much milk it produces in a day, then use this amount to calculate how much milk the cow will produce in 12 days.
GPT-4o:
First, we need to determine how much milk the cow produces in one day. We know that the cow produces 72 liters of milk in 12 days. To find the daily production, we divide the total amount of milk by the number of days: \[ \text{Daily milk production} = \frac{72 \text{ liters}}{12 \text{ days}} \] \[ \text{Daily milk production} = 6 \text{ liters/day} \] Next, we use this daily production rate to calculate how much milk the cow will produce in 12 days: \[ \text{Milk produced in 12 days} = 6 \text{ liters/day} \times 12 \text{ days} \] \[ \text{Milk produced in 12 days} = 72 \text{ liters} \] ### Answer: 72 liters
Expected answer: 72
Correct? Yes
Problem: If instead the cow produced 72 liters of milk in 10 days, and you still wanted to find out how much milk it would produce in 12 days, how much would that be?
GPT-4o:
First, we need to determine how much milk the cow produces in one day. We know that the cow produces 72 liters of milk in 10 days. To find the daily production, we divide the total amount of milk by the number of days: \[ \text{Daily milk production} = \frac{72 \text{ liters}}{10 \text{ days}} \] \[ \text{Daily milk production} = 7.2 \text{ liters/day} \] Next, we use this daily production rate to calculate how much milk the cow will produce in 12 days: \[ \text{Milk produced in 12 days} = 7.2 \text{ liters/day} \times 12 \text{ days} \] \[ \text{Milk produced in 12 days} = 86.4 \text{ liters} \] ### Answer: 86.4 liters
Expected answer: 432/5
Correct? No
Problem: On a map, 30 miles is represented as 10 inches. How many miles does 1 inch represent?
GPT-4o:
To determine how many miles 1 inch represents, we need to set up a proportion based on the given information. We know that: \[ 30 \text{ miles} = 10 \text{ inches} \] We want to find out how many miles \( x \) are represented by 1 inch. We can set up the proportion as follows: \[ \frac{30 \text{ miles}}{10 \text{ inches}} = \frac{x \text{ miles}}{1 \text{ inch}} \] To solve for \( x \), we can cross-multiply and solve the equation: \[ 30 \text{ miles} \times 1 \text{ inch} = 10 \text{ inches} \times x \text{ miles} \] \[ 30 = 10x \] Now, divide both sides by 10 to isolate \( x \): \[ x = \frac{30}{10} \] \[ x = 3 \] Therefore, 1 inch represents 3 miles on the map. ### Answer: 3 miles
Expected answer: 3
Correct? Yes
Problem: If the scale of the map is adjusted so that instead of 30 miles being represented by 10 inches, it is now represented by 12 inches, how many miles would 1 inch represent on the new map?
GPT-4o:
To determine how many miles 1 inch represents on the new map, we need to set up a proportion based on the new scale. We know that: \[ 30 \text{ miles} = 12 \text{ inches} \] We want to find out how many miles \( y \) are represented by 1 inch. We can set up the proportion as follows: \[ \frac{30 \text{ miles}}{12 \text{ inches}} = \frac{y \text{ miles}}{1 \text{ inch}} \] To solve for \( y \), we can cross-multiply and solve the equation: \[ 30 \text{ miles} \times 1 \text{ inch} = 12 \text{ inches} \times y \text{ miles} \] \[ 30 = 12y \] Now, divide both sides by 12 to isolate \( y \): \[ y = \frac{30}{12} \] \[ y = 2.5 \] Therefore, 1 inch represents 2.5 miles on the new map. ### Answer: 2.5 miles
Expected answer: 5/2
Correct? No
Problem: A truck has 8 tires. If each tire can carry a load of 8 tons, how much total load can the truck carry when all tires are fully loaded?
GPT-4o:
To determine the total load the truck can carry when all tires are fully loaded, we need to multiply the number of tires by the load each tire can carry. The truck has 8 tires, and each tire can carry a load of 8 tons. Therefore, the total load the truck can carry is calculated as follows: \[ \text{Total load} = \text{Number of tires} \times \text{Load per tire} \] \[ \text{Total load} = 8 \times 8 \] \[ \text{Total load} = 64 \text{ tons} \] ### Answer: 64 tons
Expected answer: 64
Correct? Yes
Problem: If the truck with all the tires fully loaded is carrying cargo weighing the same as the total load the tires can handle, what would be the total weight being carried by the truck?
GPT-4o:
If the truck is carrying cargo that weighs the same as the total load the tires can handle, we need to consider the total load capacity we calculated previously. From the previous calculation, we know that the total load the truck can carry when all tires are fully loaded is 64 tons. Therefore, if the truck is carrying cargo weighing the same as the total load capacity, the total weight being carried by the truck is: ### Answer: 64 tons
Expected answer: 64
Correct? Yes
Problem: In the previous scenario, each tire was capable of carrying a load of 8 tons. But what if each tire was only capable of carrying a load of 3 tons? How much total load could the truck carry then when all tires are fully loaded?
GPT-4o:
To determine the total load the truck can carry when each tire is capable of carrying a load of 3 tons, we need to multiply the number of tires by the load each tire can carry. The truck has 8 tires, and each tire can carry a load of 3 tons. Therefore, the total load the truck can carry is calculated as follows: \[ \text{Total load} = \text{Number of tires} \times \text{Load per tire} \] \[ \text{Total load} = 8 \times 3 \] \[ \text{Total load} = 24 \text{ tons} \] ### Answer: 24 tons
Expected answer: 24
Correct? Yes
Problem: If you have 4 fruits and each fruit provides 1 cup of juice, how many cups of juice can you get in total?
GPT-4o:
To determine the total number of cups of juice, we need to multiply the number of fruits by the amount of juice each fruit provides. Given: - Number of fruits = 4 - Juice per fruit = 1 cup Calculation: \[ 4 \text{ fruits} \times 1 \text{ cup per fruit} = 4 \text{ cups of juice} \] ### Answer: 4 cups of juice.
Expected answer: 4
Correct? Yes
Problem: If instead you started with just 1 fruit, how many cups of juice would you be able to make?
GPT-4o:
Given that each fruit provides 1 cup of juice, if you start with just 1 fruit, you would be able to make: \[ 1 \text{ fruit} \times 1 \text{ cup per fruit} = 1 \text{ cup of juice} \] ### Answer: 1 cup of juice.
Expected answer: 1
Correct? Yes
Problem: Sara has a box of colored pencils, and she has 5 colors. If she has 5 of each type, how many colored pencils does Sara have in total?
GPT-4o:
To determine the total number of colored pencils Sara has, we need to multiply the number of colors by the number of pencils of each color. Sara has 5 colors, and she has 5 pencils of each color. Therefore, we calculate the total number of pencils as follows: \[ \text{Total number of pencils} = \text{Number of colors} \times \text{Number of pencils per color} \] \[ \text{Total number of pencils} = 5 \times 5 \] \[ \text{Total number of pencils} = 25 \] ### Answer: 25
Expected answer: 25
Correct? Yes
Problem: Sara decided to duplicate her complete set of colored pencils and she bought exactly the same amount as she had. Now, how many colored pencils does Sara have in total?
GPT-4o:
Initially, Sara had 25 colored pencils. If she decided to duplicate her complete set, she bought an additional 25 colored pencils. To find the total number of colored pencils Sara has now, we add the original number of pencils to the number of pencils she bought: \[ \text{Total number of pencils} = \text{Original number of pencils} + \text{Duplicated set of pencils} \] \[ \text{Total number of pencils} = 25 + 25 \] \[ \text{Total number of pencils} = 50 \] ### Answer: 50
Expected answer: 50
Correct? Yes
Problem: Sara suddenly realized that she had miscalculated; she actually has 11 of each type of colored pencil, not 5. With this correction, how many colored pencils does Sara really have?
GPT-4o:
To determine the corrected total number of colored pencils Sara has, we need to multiply the number of colors by the corrected number of pencils of each color. Sara has 5 colors, and she now realizes she has 11 pencils of each color. Therefore, we calculate the total number of pencils as follows: \[ \text{Total number of pencils} = \text{Number of colors} \times \text{Number of pencils per color} \] \[ \text{Total number of pencils} = 5 \times 11 \] \[ \text{Total number of pencils} = 55 \] ### Answer: 55
Expected answer: 55
Correct? Yes
Problem: In a word, each letter corresponds to a point in a game. If you have a 12-letter word, how many points will you get if each letter corresponds to 1 point in the game?
GPT-4o:
To determine the total points for a 12-letter word where each letter corresponds to 1 point, we simply multiply the number of letters by the points per letter. \[ 12 \text{ letters} \times 1 \text{ point per letter} = 12 \text{ points} \] ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: You have decided to play 8 rounds of the same game. If you continue to use the same 12-letter word in each round, how many points will you accumulate in total from all the rounds?
GPT-4o:
To find the total points accumulated from playing 8 rounds using the same 12-letter word, we need to multiply the points per round by the number of rounds. From the previous problem, we know that a 12-letter word gives 12 points per round. \[ 12 \text{ points per round} \times 8 \text{ rounds} = 96 \text{ points} \] ### Answer: 96
Expected answer: 96
Correct? Yes
Problem: You decide to change your strategy in the next game and instead use a 9-letter word. If each letter still corresponds to 1 point, how many points will you get in this game?
GPT-4o:
To determine the total points for a 9-letter word where each letter corresponds to 1 point, we multiply the number of letters by the points per letter. \[ 9 \text{ letters} \times 1 \text{ point per letter} = 9 \text{ points} \] ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Jake has 7 crates, each containing 7 bottles of water. How many bottles of water does he have in total?
GPT-4o:
To determine the total number of bottles of water Jake has, we need to multiply the number of crates by the number of bottles in each crate. Jake has 7 crates, and each crate contains 7 bottles of water. Therefore, we calculate: \[ 7 \text{ crates} \times 7 \text{ bottles per crate} = 49 \text{ bottles} \] ### Answer: 49
Expected answer: 49
Correct? Yes
Problem: Jake decided to not drink any of the water just yet and stored all the bottles in his garage. After leaving the bottles in the garage untouched, how many bottles does Jake still have?
GPT-4o:
Since Jake decided not to drink any of the water and stored all the bottles in his garage, the number of bottles remains unchanged. Jake originally had 49 bottles of water, and since he hasn't consumed any, he still has: ### Answer: 49
Expected answer: 49
Correct? Yes
Problem: A piano has 4 legs. If there are 2 pianos in the music room, how many legs are there in total?
GPT-4o:
To determine the total number of legs for 2 pianos, we start by noting that each piano has 4 legs. First, calculate the number of legs for one piano: \[ 4 \text{ legs/piano} \] Since there are 2 pianos, we multiply the number of legs per piano by the number of pianos: \[ 4 \text{ legs/piano} \times 2 \text{ pianos} = 8 \text{ legs} \] ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: Considering from the previous question, what if each piano only had 3 legs instead of 4. With 2 pianos in the music room, how many legs would there be in total?
GPT-4o:
To determine the total number of legs for 2 pianos, each with 3 legs, we start by noting that each piano has 3 legs. First, calculate the number of legs for one piano: \[ 3 \text{ legs/piano} \] Since there are 2 pianos, we multiply the number of legs per piano by the number of pianos: \[ 3 \text{ legs/piano} \times 2 \text{ pianos} = 6 \text{ legs} \] ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: A keyring holds 2 keys but each keyring must be split between two people. How many keys does each person get?
GPT-4o:
To determine how many keys each person gets, we need to divide the total number of keys by the number of people sharing them. Given: - A keyring holds 2 keys. - The keyring must be split between two people. So, we divide the 2 keys by 2 people: \[ \frac{2 \text{ keys}}{2 \text{ people}} = 1 \text{ key per person} \] ### Answer: 1 key per person.
Expected answer: 1
Correct? Yes
Problem: Following the previous scenario, if there are 11 keyrings in total, how many keys does each person get?
GPT-4o:
First, we need to determine the total number of keys. Since each keyring holds 2 keys and there are 11 keyrings, we calculate: \[ 11 \text{ keyrings} \times 2 \text{ keys per keyring} = 22 \text{ keys} \] Next, we need to divide these 22 keys between two people: \[ \frac{22 \text{ keys}}{2 \text{ people}} = 11 \text{ keys per person} \] ### Answer: 11 keys per person.
Expected answer: 11
Correct? Yes
Problem: In the previous scenario, suppose now that each keyring holds 3 keys, but still has to be split amongst two people. How many keys does each person get now?
GPT-4o:
To determine how many keys each person gets when a keyring holds 3 keys and must be split between two people, we divide the total number of keys by the number of people sharing them. Given: - A keyring holds 3 keys. - The keyring must be split between two people. So, we divide the 3 keys by 2 people: \[ \frac{3 \text{ keys}}{2 \text{ people}} = 1.5 \text{ keys per person} \] ### Answer: 1.5 keys per person.
Expected answer: 3/2
Correct? No
Problem: Javier has 9 crates of bottles. Each crate contains 6 bottles, how many bottles does Javier have?
GPT-4o:
To determine the total number of bottles Javier has, we need to multiply the number of crates by the number of bottles per crate. Given: - Number of crates = 9 - Number of bottles per crate = 6 Calculation: \[ \text{Total number of bottles} = \text{Number of crates} \times \text{Number of bottles per crate} \] \[ \text{Total number of bottles} = 9 \times 6 \] \[ \text{Total number of bottles} = 54 \] ### Answer: 54
Expected answer: 54
Correct? Yes
Problem: Javier decided to pack more bottles into his crates. Now, each crate contains 8 bottles instead of 6. How many bottles does Javier have now with his 9 crates?
GPT-4o:
To determine the new total number of bottles Javier has, we need to multiply the number of crates by the new number of bottles per crate. Given: - Number of crates = 9 - New number of bottles per crate = 8 Calculation: \[ \text{Total number of bottles} = \text{Number of crates} \times \text{New number of bottles per crate} \] \[ \text{Total number of bottles} = 9 \times 8 \] \[ \text{Total number of bottles} = 72 \] ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: A shirt costs 10 dollars. If 1 dollar equals 1 euro, how much does the shirt cost in euros?
GPT-4o:
Since 1 dollar equals 1 euro, the cost of the shirt in euros is the same as its cost in dollars. The shirt costs 10 dollars, so it will also cost 10 euros. ### Answer: 10 euros.
Expected answer: 10
Correct? Yes
Problem: Following the previous question: if the exchange rate changes and now 1 euro equals 1 dollar, how much will the shirt cost in dollars now?
GPT-4o:
If the exchange rate changes such that 1 euro equals 1 dollar, the cost of the shirt in dollars remains unchanged because the exchange rate is still 1:1. Therefore, the shirt will still cost 10 dollars. ### Answer: 10 dollars.
Expected answer: 10
Correct? Yes
Problem: After the price changes, the shirt now costs 9 dollars. If 1 dollar equals 1 euro, how much does the shirt cost in euros now?
GPT-4o:
Since 1 dollar equals 1 euro, the cost of the shirt in euros is the same as its cost in dollars. The shirt now costs 9 dollars, so it will also cost 9 euros. ### Answer: 9 euros.
Expected answer: 9
Correct? Yes
Problem: If a plant grows 12 flowers each month, how many flowers will it grow in 5 months?
GPT-4o:
To determine how many flowers the plant will grow in 5 months, we need to multiply the number of flowers it grows each month by the number of months. Given: - The plant grows 12 flowers each month. - We want to find the total number of flowers grown in 5 months. Calculation: \[ 12 \text{ flowers/month} \times 5 \text{ months} = 60 \text{ flowers} \] ### Answer: 60
Expected answer: 60
Correct? Yes
Problem: A beach ball is being blown up to be twice the size of its original size of 3 feet in diameter. What will be the diameter of the beach ball after it is blown up?
GPT-4o:
To determine the new diameter of the beach ball after it is blown up to twice its original size, we need to multiply the original diameter by 2. The original diameter of the beach ball is 3 feet. New diameter = 2 * original diameter New diameter = 2 * 3 feet New diameter = 6 feet ### Answer: 6 feet
Expected answer: 6
Correct? Yes
Problem: Suppose the original size of the beach ball was actually 5 feet in diameter, not 3 feet as previously stated. If it is still being blown up to be twice its original size, what will be the diameter of the beach ball after it is blown up now?
GPT-4o:
To determine the new diameter of the beach ball after it is blown up to twice its original size, we need to multiply the original diameter by 2. The original diameter of the beach ball is 5 feet. New diameter = 2 * original diameter New diameter = 2 * 5 feet New diameter = 10 feet ### Answer: 10 feet
Expected answer: 10
Correct? Yes
Problem: A farmer has a total of 24 tomatoes. He wants to equally divide them into 4 boxes. How many tomatoes will there be in each box?
GPT-4o:
To determine how many tomatoes will be in each box, we need to divide the total number of tomatoes by the number of boxes. The total number of tomatoes is 24, and the number of boxes is 4. We perform the division: \[ \frac{24}{4} = 6 \] So, each box will contain 6 tomatoes. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: The farmer then decides to combine all the tomatoes from the 4 boxes back into one large container. How many tomatoes will there be in the large container?
GPT-4o:
Since the farmer initially divided the 24 tomatoes equally into 4 boxes, each box contains 6 tomatoes. To find the total number of tomatoes when they are combined back into one large container, we simply add the tomatoes from all 4 boxes together: \[ 6 \text{ tomatoes/box} \times 4 \text{ boxes} = 24 \text{ tomatoes} \] Thus, the large container will have 24 tomatoes. ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: In a different scenario, if the farmer had decided to equally divide the 24 tomatoes between only 2 boxes instead of 4, how many tomatoes would have been in each box then?
GPT-4o:
To determine how many tomatoes will be in each box when dividing 24 tomatoes between 2 boxes, we need to perform the division: \[ \frac{24}{2} = 12 \] So, each box will contain 12 tomatoes. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: John wants to go out playing with his scooter. He travels a certain distance "B" which he calculates as half of 16. When he gets tired, he multiplies the distance "B" he traveled with 6 to find out the total distance "X" he traveled back and forth in his playing area. What is the total distance "X" he traveled?
GPT-4o:
First, we need to determine the distance "B" that John travels initially. According to the problem, "B" is half of 16. \[ B = \frac{16}{2} = 8 \] Next, John multiplies this distance "B" by 6 to find the total distance "X" he traveled back and forth. \[ X = B \times 6 = 8 \times 6 = 48 \] ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: In the previous situation, John multiplied the distance he traveled with 6. But this time, he decides to ride his scooter for a bit longer. Instead of multiplying by 6, he now multiplies the same initial half of 16, distance "B", by 8 to find out the new total distance "X" he traveled back and forth. What is the new total distance "X" he traveled?
GPT-4o:
First, we determine the distance "B" that John travels initially, which is half of 16. \[ B = \frac{16}{2} = 8 \] Now, John multiplies this distance "B" by 8 to find the new total distance "X" he traveled back and forth. \[ X = B \times 8 = 8 \times 8 = 64 \] ### Answer: 64
Expected answer: 64
Correct? Yes
Problem: Lisa has a favorite TV show that she likes to watch, which happens to be 8 minutes long per episode. If Lisa decides to watch 2 episodes back-to-back without any breaks, how long will she be watching her favorite TV show in total?
GPT-4o:
To determine the total time Lisa will spend watching her favorite TV show, we need to multiply the duration of one episode by the number of episodes she watches. Each episode is 8 minutes long, and Lisa watches 2 episodes back-to-back. Total time = Duration of one episode Γ Number of episodes Total time = 8 minutes/episode Γ 2 episodes Total time = 16 minutes ### Answer: 16 minutes
Expected answer: 16
Correct? Yes
Problem: Now, imagine Lisa spent 5 days over the course of a week doing the same routine of watching 2 episodes back-to-back of her favorite TV show, which is 8 minutes per episode. How long in total did she spend watching her TV show over those 5 days?
GPT-4o:
First, we calculate the total time Lisa spends watching her TV show in one day. As previously determined, watching 2 episodes back-to-back takes 16 minutes. Next, we need to find out how much time she spends over 5 days. Total time per day = 16 minutes Number of days = 5 Total time over 5 days = Total time per day Γ Number of days Total time over 5 days = 16 minutes/day Γ 5 days Total time over 5 days = 80 minutes ### Answer: 80 minutes
Expected answer: 80
Correct? Yes
Problem: In a twist, one day Lisa decided to watch a different TV show, which is 12 minutes long per episode. If she watches 2 episodes of this show back-to-back without any breaks, how long will she be watching this different TV show in total?
GPT-4o:
To determine the total time Lisa will spend watching the different TV show, we need to multiply the duration of one episode by the number of episodes she watches. Each episode of the different TV show is 12 minutes long, and Lisa watches 2 episodes back-to-back. Total time = Duration of one episode Γ Number of episodes Total time = 12 minutes/episode Γ 2 episodes Total time = 24 minutes ### Answer: 24 minutes
Expected answer: 24
Correct? Yes
Problem: Jane has 1 blanket and John has 3 times as many blankets as Jane. How many blankets does John have?
GPT-4o:
To determine how many blankets John has, we need to multiply the number of blankets Jane has by 3. Jane has 1 blanket. Therefore, John has: \[ 1 \text{ blanket} \times 3 = 3 \text{ blankets} \] ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: Consider the starting point of the previous problem where Jane had 1 blanket and John had 3 times as many blankets as Jane. Now, suppose that Jane initially has 6 blankets instead of 1. In this new scenario, how many blankets does John have initially?
GPT-4o:
To determine how many blankets John has in the new scenario, we need to multiply the number of blankets Jane has by 3. Jane now has 6 blankets. Therefore, John has: \[ 6 \text{ blankets} \times 3 = 18 \text{ blankets} \] ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: John has $28 which he wants to divide equally among his 7 children. How many dollars will each child receive?
GPT-4o:
To determine how many dollars each child will receive, we need to divide the total amount of money by the number of children. Given: - Total amount of money = $28 - Number of children = 7 We perform the division: \[ \frac{28}{7} = 4 \] So, each child will receive $4. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: If John originally had $10 instead of $28, and he still wanted to divide it equally among his 7 children, how much would each child receive now?
GPT-4o:
To determine how many dollars each child will receive, we need to divide the total amount of money by the number of children. Given: - Total amount of money = $10 - Number of children = 7 We perform the division: \[ \frac{10}{7} \approx 1.4286 \] So, each child will receive approximately $1.43 when rounded to the nearest cent. ### Answer: 1.43
Expected answer: 10/7
Correct? No
Problem: A tailor uses 2 meters of fabric to make one shirt. He uses double the fabric for the shirt's lining. If the tailor wants to make 5 shirts with lining, how many meters of fabric will he use for the lining?
GPT-4o:
To determine the amount of fabric the tailor will use for the lining, we need to consider the following: 1. The tailor uses 2 meters of fabric for one shirt. 2. The lining requires double the fabric used for the shirt. First, calculate the fabric needed for the lining of one shirt: \[ \text{Fabric for lining of one shirt} = 2 \times 2 = 4 \text{ meters} \] Next, since the tailor wants to make 5 shirts with lining, we multiply the fabric needed for the lining of one shirt by 5: \[ \text{Total fabric for lining of 5 shirts} = 4 \times 5 = 20 \text{ meters} \] ### Answer: 20 meters
Expected answer: 20
Correct? Yes
Problem: Kate owns a scooter shop. She sells 1 scooter every day. How many scooters will she sell after 8 days?
GPT-4o:
To determine how many scooters Kate will sell after 8 days, we need to multiply the number of scooters she sells per day by the number of days. Kate sells 1 scooter per day. Therefore, in 8 days, she will sell: \[ 1 \text{ scooter/day} \times 8 \text{ days} = 8 \text{ scooters} \] ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: Continuing from the previous situation, after selling 1 scooter a day for 8 days, Kate decides to hold a grand sale for 8 more days where she sells the same number of scooters she sold in the previous 8 days every day. How many additional scooters will she sell during this grand sale?
GPT-4o:
To determine how many additional scooters Kate will sell during the grand sale, we need to calculate the number of scooters she sells each day during the grand sale and then multiply that by the number of days the sale lasts. From the previous situation, we know that Kate sold 8 scooters in the first 8 days. During the grand sale, she sells the same number of scooters each day as she sold in the previous 8 days, which is 8 scooters per day. The grand sale lasts for 8 days, so the total number of additional scooters she will sell is: \[ 8 \text{ scooters/day} \times 8 \text{ days} = 64 \text{ scooters} \] ### Answer: 64
Expected answer: 64
Correct? Yes
Problem: Let's revise the original situation. Instead of selling 1 scooter a day, let's say Kate was actually selling 7 scooters a day for 8 days. How many scooters did she sell in this period?
GPT-4o:
To determine how many scooters Kate sold in 8 days, given that she sells 7 scooters per day, we need to multiply the number of scooters sold per day by the number of days. Kate sells 7 scooters per day. Therefore, in 8 days, she will sell: \[ 7 \text{ scooters/day} \times 8 \text{ days} = 56 \text{ scooters} \] ### Answer: 56
Expected answer: 56
Correct? Yes
Problem: In a forest, one tree produces 10 seeds each year. How many seeds does the tree produce in 1 year?
GPT-4o:
To determine how many seeds the tree produces in one year, we simply need to use the given information that one tree produces 10 seeds each year. Thus, the number of seeds produced by the tree in one year is: \[ 10 \text{ seeds/year} \] ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: Now imagine that the tree actually produces 12 seeds each year instead of 10. How many seeds does the tree produce in 1 year?
GPT-4o:
Given that the tree produces 12 seeds each year, we can directly state the number of seeds produced in one year. Thus, the number of seeds produced by the tree in one year is: \[ 12 \text{ seeds/year} \] ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: The sun shines 12 hours in a day and a scientist wants to divide it into 6 equal parts for an experiment. How many hours are there in each part?
GPT-4o:
To determine how many hours are in each part, we need to divide the total number of hours the sun shines in a day by the number of parts the scientist wants to divide it into. The sun shines for 12 hours in a day, and the scientist wants to divide this into 6 equal parts. We perform the division: \[ \frac{12 \text{ hours}}{6 \text{ parts}} = 2 \text{ hours per part} \] ### Answer: 2 hours per part.
Expected answer: 2
Correct? Yes
Problem: A group of 12 friends decided to split into smaller groups to play a board game. If they want to have exactly 3 friends in each group, how many groups will there be?
GPT-4o:
To determine how many groups of 3 friends can be formed from a total of 12 friends, we need to divide the total number of friends by the number of friends per group. \[ \text{Number of groups} = \frac{\text{Total number of friends}}{\text{Number of friends per group}} = \frac{12}{3} \] Performing the division: \[ \frac{12}{3} = 4 \] So, there will be 4 groups. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: Following the same scenario where the friends were divided into groups, if each group decided to buy 7 pizzas, how many pizzas would be bought in total?
GPT-4o:
We already determined that there are 4 groups of friends. If each group buys 7 pizzas, we need to calculate the total number of pizzas by multiplying the number of groups by the number of pizzas each group buys. \[ \text{Total number of pizzas} = \text{Number of groups} \times \text{Number of pizzas per group} = 4 \times 7 \] Performing the multiplication: \[ 4 \times 7 = 28 \] So, the total number of pizzas bought will be 28. ### Answer: 28
Expected answer: 28
Correct? Yes
Problem: Continuing from our previous scenario, let's say that instead of having 12 friends, there were actually only 6 friends to begin with. If they still want to divide themselves into groups with 3 friends each, how many group will there be?
GPT-4o:
To determine how many groups of 3 friends can be formed from a total of 6 friends, we need to divide the total number of friends by the number of friends per group. \[ \text{Number of groups} = \frac{\text{Total number of friends}}{\text{Number of friends per group}} = \frac{6}{3} \] Performing the division: \[ \frac{6}{3} = 2 \] So, there will be 2 groups. ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: Emma and her friends are building sandcastles on the beach. Each sandcastle uses 6 buckets of sand, and they build 4 sandcastles. Each bucket of sand has 3 shovels full of sand in it. How many shovels of sand do they use in total?
GPT-4o:
First, we need to determine the total number of buckets of sand used for the sandcastles. Each sandcastle uses 6 buckets of sand, and they build 4 sandcastles: \[ 6 \text{ buckets/sandcastle} \times 4 \text{ sandcastles} = 24 \text{ buckets} \] Next, we need to find out how many shovels of sand are in each bucket. Each bucket contains 3 shovels full of sand: \[ 3 \text{ shovels/bucket} \] Now, we multiply the total number of buckets by the number of shovels per bucket to find the total number of shovels of sand used: \[ 24 \text{ buckets} \times 3 \text{ shovels/bucket} = 72 \text{ shovels} \] ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: Continuing from the previous situation, Emma and her friends decide to make their sandcastles stronger. They pour a layer of seawater on each shovel used in their sandcastles. If each shovel full of sand requires 1 bottle of seawater, how many bottles of seawater will they need in total?
GPT-4o:
From the previous calculation, we know that Emma and her friends used a total of 72 shovels of sand. Since each shovel full of sand requires 1 bottle of seawater, the number of bottles of seawater needed is equal to the number of shovels of sand. Therefore, they will need: \[ 72 \text{ shovels} \times 1 \text{ bottle/shovel} = 72 \text{ bottles} \] ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: Following the previous situation with Emma and her friends building sandcastles, imagine that they had originally started with 5 sandcastles instead of 6. Each of these 5 sandcastles still uses 4 buckets of sand and each of these buckets contains 3 shovels of sand. How many shovels of sand would they have used then?
GPT-4o:
First, we need to determine the total number of buckets of sand used for the sandcastles. Each sandcastle uses 4 buckets of sand, and they build 5 sandcastles: \[ 4 \text{ buckets/sandcastle} \times 5 \text{ sandcastles} = 20 \text{ buckets} \] Next, we need to find out how many shovels of sand are in each bucket. Each bucket contains 3 shovels full of sand: \[ 3 \text{ shovels/bucket} \] Now, we multiply the total number of buckets by the number of shovels per bucket to find the total number of shovels of sand used: \[ 20 \text{ buckets} \times 3 \text{ shovels/bucket} = 60 \text{ shovels} \] ### Answer: 60
Expected answer: 60
Correct? Yes
Problem: Jenna is making bracelets for her friends. Each bracelet requires 12 beads and she has a total of 8 bracelets to make. How many beads will Jenna need in total?
GPT-4o:
To determine the total number of beads Jenna will need, we need to multiply the number of beads required for each bracelet by the total number of bracelets she plans to make. Each bracelet requires 12 beads, and Jenna needs to make 8 bracelets. Therefore, we calculate: \[ 12 \text{ beads/bracelet} \times 8 \text{ bracelets} = 96 \text{ beads} \] ### Answer: 96
Expected answer: 96
Correct? Yes
Problem: After reconsidering, Jenna decided to only make 7 bracelets instead of 8. Now, how many beads will Jenna need to make the bracelets?
GPT-4o:
To determine the total number of beads Jenna will need after deciding to make 7 bracelets, we need to multiply the number of beads required for each bracelet by the new total number of bracelets. Each bracelet requires 12 beads, and Jenna now plans to make 7 bracelets. Therefore, we calculate: \[ 12 \text{ beads/bracelet} \times 7 \text{ bracelets} = 84 \text{ beads} \] ### Answer: 84
Expected answer: 84
Correct? Yes
Problem: Penny has 66 milliliters of toothpaste in a new tube. If she uses 11 milliliters for each brushing, how many times can she brush her teeth with the new tube of toothpaste?
GPT-4o:
To determine how many times Penny can brush her teeth with the new tube of toothpaste, we need to divide the total amount of toothpaste by the amount used per brushing. Given: - Total toothpaste: 66 milliliters - Toothpaste used per brushing: 11 milliliters We perform the division: \[ \frac{66 \text{ milliliters}}{11 \text{ milliliters per brushing}} = 6 \] So, Penny can brush her teeth 6 times with the new tube of toothpaste. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: If Penny started using 9 milliliters of toothpaste for each brushing instead of 11, how many times could she brush her teeth with the new tube of toothpaste?
GPT-4o:
To determine how many times Penny can brush her teeth with the new tube of toothpaste when using 9 milliliters per brushing, we need to divide the total amount of toothpaste by the new amount used per brushing. Given: - Total toothpaste: 66 milliliters - Toothpaste used per brushing: 9 milliliters We perform the division: \[ \frac{66 \text{ milliliters}}{9 \text{ milliliters per brushing}} = 7.33 \] Since Penny cannot brush her teeth a fraction of a time, we take the whole number part of the result, which is 7. So, Penny can brush her teeth 7 times with the new tube of toothpaste when using 9 milliliters per brushing. ### Answer: 7
Expected answer: 22/3
Correct? No
Problem: Vanessa has 4 bunches of grapes and each bunch has 11 grapes. How many grapes does Vanessa have in total?
GPT-4o:
To find the total number of grapes Vanessa has, we need to multiply the number of bunches by the number of grapes in each bunch. Vanessa has 4 bunches of grapes, and each bunch contains 11 grapes. Therefore, we calculate: \[ 4 \text{ bunches} \times 11 \text{ grapes per bunch} = 44 \text{ grapes} \] ### Answer: 44
Expected answer: 44
Correct? Yes
Problem: If Vanessa only had 4 bunches of grapes and each bunch had 5 grapes instead of 11, how many grapes would Vanessa have in total then?
GPT-4o:
To find the total number of grapes Vanessa would have if each bunch had 5 grapes, we need to multiply the number of bunches by the number of grapes in each bunch. Vanessa has 4 bunches of grapes, and each bunch contains 5 grapes. Therefore, we calculate: \[ 4 \text{ bunches} \times 5 \text{ grapes per bunch} = 20 \text{ grapes} \] ### Answer: 20
Expected answer: 20
Correct? Yes
Problem: Mary has a length of fabric measuring 6 yards. She needs 6 yards of fabric to make a skirt. How many skirts can she make with the fabric she has?
GPT-4o:
To determine how many skirts Mary can make with her 6 yards of fabric, we need to divide the total length of fabric by the amount of fabric required for one skirt. Given: - Total fabric Mary has = 6 yards - Fabric needed for one skirt = 6 yards We perform the division: \[ \text{Number of skirts} = \frac{\text{Total fabric}}{\text{Fabric per skirt}} = \frac{6 \text{ yards}}{6 \text{ yards/skirt}} = 1 \] ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: Mary used her 6 yards of fabric to make a skirt. Each skirt she makes, requires 6 yards of fabric. She decides to make as many skirts as skirts she already made (i.e., she wants to multiply the number of skirts by the number of skirts she already made). How many skirts will Mary have made in total?
GPT-4o:
First, let's determine how many skirts Mary initially made with her 6 yards of fabric. As calculated previously, she made 1 skirt. Now, Mary decides to make as many skirts as the number of skirts she already made. Since she initially made 1 skirt, she will now make 1 more skirt. To find the total number of skirts she will have made, we add the initial number of skirts to the additional skirts she plans to make: \[ \text{Total number of skirts} = \text{Initial skirts} + \text{Additional skirts} = 1 + 1 = 2 \] ### Answer: 2
Expected answer: 1
Correct? No
Problem: Mary now has a new length of fabric that's 7 yards long. Keeping in mind that each skirt requires 6 yards of fabric, how many skirts can Mary make with the new fabric she has?
GPT-4o:
To determine how many skirts Mary can make with her 7 yards of fabric, we need to divide the total length of fabric by the amount of fabric required for one skirt. Given: - Total fabric Mary has = 7 yards - Fabric needed for one skirt = 6 yards We perform the division: \[ \text{Number of skirts} = \frac{\text{Total fabric}}{\text{Fabric per skirt}} = \frac{7 \text{ yards}}{6 \text{ yards/skirt}} \approx 1.1667 \] Since Mary cannot make a fraction of a skirt with the given fabric, she can only make 1 complete skirt. ### Answer: 1
Expected answer: 7/6
Correct? No
Problem: Jordan has 9 card packs and each pack contains 1 card. If he decides to double the total number of his cards, how many cards will Jordan have then?
GPT-4o:
First, we determine the total number of cards Jordan currently has. Since each of the 9 card packs contains 1 card, Jordan has: \[ 9 \times 1 = 9 \text{ cards} \] Next, Jordan decides to double the total number of his cards. Therefore, we calculate: \[ 2 \times 9 = 18 \text{ cards} \] ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: Following up from the previous question, if Jordan decides to again double the total number of cards he has, how many cards will Jordan end up with at that point?
GPT-4o:
From the previous calculation, we know that Jordan has 18 cards after doubling his initial number of cards. If Jordan decides to double the total number of his cards again, we calculate: \[ 2 \times 18 = 36 \text{ cards} \] ### Answer: 36
Expected answer: 36
Correct? Yes
Problem: Following up from the previous question, if originally Jordan had 5 card packs instead of 9, and he still decided to double the total number of his cards, how many cards would Jordan have then?
GPT-4o:
First, we determine the total number of cards Jordan would have if he originally had 5 card packs, with each pack containing 1 card. Therefore, Jordan has: \[ 5 \times 1 = 5 \text{ cards} \] Next, Jordan decides to double the total number of his cards. Therefore, we calculate: \[ 2 \times 5 = 10 \text{ cards} \] ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: A wizard casts a magic spell that lasts 60 minutes. However, his wizard staff can only channel the spell for 6 equal periods of time before it needs a 1-minute break to recharge. How long is each period of the spell?
GPT-4o:
To determine the length of each period of the spell, we need to divide the total duration of the spell by the number of periods. The total duration of the spell is 60 minutes, and the spell is divided into 6 equal periods. We calculate the length of each period by dividing the total duration by the number of periods: \[ \text{Length of each period} = \frac{60 \text{ minutes}}{6} \] \[ \text{Length of each period} = 10 \text{ minutes} \] ### Answer: 10 minutes
Expected answer: 10
Correct? Yes
Problem: In the magical world, a donezal is a unit of time equal to 10 wizard staff channeling periods. If every wizard staff channeling period lasts as long as the spell in the previous problem, how much time does one donezal represent?
GPT-4o:
From the previous problem, we know that each wizard staff channeling period lasts 10 minutes. A donezal is defined as 10 wizard staff channeling periods. Therefore, to find the total time represented by one donezal, we multiply the duration of one period by 10: \[ \text{Time for one donezal} = 10 \text{ periods} \times 10 \text{ minutes per period} \] \[ \text{Time for one donezal} = 100 \text{ minutes} \] ### Answer: 100 minutes
Expected answer: 100
Correct? Yes
Problem: In a new experiment, the wizard decided to divide the same 60-minute spell into only 4 equal periods before the wizard staff needs to take a break. How long does each period of casting last now?
GPT-4o:
To determine the length of each period of the spell when it is divided into 4 equal periods, we need to divide the total duration of the spell by the number of periods. The total duration of the spell is 60 minutes, and the spell is divided into 4 equal periods. We calculate the length of each period by dividing the total duration by the number of periods: \[ \text{Length of each period} = \frac{60 \text{ minutes}}{4} \] \[ \text{Length of each period} = 15 \text{ minutes} \] ### Answer: 15 minutes
Expected answer: 15
Correct? Yes
Problem: A drummer hits his drum 11 times per minute. How many times does he hit the drum in 8 minutes?
GPT-4o:
To determine how many times the drummer hits the drum in 8 minutes, we need to multiply the number of hits per minute by the number of minutes. The drummer hits the drum 11 times per minute. Therefore, in 8 minutes, he hits the drum: \[ 11 \text{ hits/minute} \times 8 \text{ minutes} = 88 \text{ hits} \] ### Answer: 88
Expected answer: 88
Correct? Yes
Problem: In the previous problem, the drummer was hitting his drum 11 times per minute. But what if his rhythm slows down and he now hits the drum only 2 times per minute. How many times will he hit the drum in 8 minutes then?
GPT-4o:
To determine how many times the drummer hits the drum in 8 minutes at the new rhythm, we need to multiply the number of hits per minute by the number of minutes. The drummer now hits the drum 2 times per minute. Therefore, in 8 minutes, he hits the drum: \[ 2 \text{ hits/minute} \times 8 \text{ minutes} = 16 \text{ hits} \] ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: John is packing for a trip and realizes that for each pair of pants, he needs 2 pairs of socks. If he plans to bring 22 pairs of socks, how many pairs of pants should he pack?
GPT-4o:
To determine how many pairs of pants John should pack, we need to use the given relationship between the pairs of pants and pairs of socks. Specifically, for each pair of pants, John needs 2 pairs of socks. Given: - John plans to bring 22 pairs of socks. - Each pair of pants requires 2 pairs of socks. We can set up the following equation to find the number of pairs of pants (let's call this number \( p \)): \[ 2p = 22 \] To solve for \( p \), we divide both sides of the equation by 2: \[ p = \frac{22}{2} \] \[ p = 11 \] Thus, John should pack 11 pairs of pants. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: Now, John is reconsidering his packing strategy. Instead of packing two pairs of socks per pair of pants, he thinks he only needs to pack two socks for every pair of pants. If he sticks to this new strategy, how many pairs of pants should he pack for his 4 pairs of socks?
GPT-4o:
In this new strategy, John needs to pack two individual socks (which is equivalent to one pair of socks) for each pair of pants. Given that he has 4 pairs of socks, we need to determine how many pairs of pants he should pack. Since each pair of pants requires 2 individual socks (or 1 pair of socks), we can set up the following relationship: \[ \text{Number of pairs of pants} = \text{Number of pairs of socks} \] Given: - John has 4 pairs of socks. Therefore, the number of pairs of pants he should pack is: \[ \text{Number of pairs of pants} = 4 \] ### Answer: 4
Expected answer: 2
Correct? No
Problem: If a pack of pens contains 8 pens and John has 5 packs, how many pens does he have in total?
GPT-4o:
To determine the total number of pens John has, we need to multiply the number of pens in each pack by the number of packs he has. Each pack contains 8 pens, and John has 5 packs. Therefore, we calculate: \[ 8 \text{ pens/pack} \times 5 \text{ packs} = 40 \text{ pens} \] ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: If, instead of 8 pens per pack, there were 6 pens per pack, how many pens would John have in total with his 5 packs?
GPT-4o:
To find the total number of pens John would have if each pack contained 6 pens, we need to multiply the number of pens per pack by the number of packs he has. Each pack contains 6 pens, and John has 5 packs. Therefore, we calculate: \[ 6 \text{ pens/pack} \times 5 \text{ packs} = 30 \text{ pens} \] ### Answer: 30
Expected answer: 30
Correct? Yes
Problem: Captain Blackbeard's pirate ship sailed for 60 hours and he divided the total hours equally among the 6 shifts. If each guard is expected to protect the ship for one shift, how many hours will one guard have to protect the ship?
GPT-4o:
To determine how many hours one guard will have to protect the ship, we need to divide the total number of hours by the number of shifts. Total hours sailed: 60 hours Number of shifts: 6 We perform the division: \[ \frac{60 \text{ hours}}{6 \text{ shifts}} = 10 \text{ hours per shift} \] Thus, each guard will have to protect the ship for 10 hours. ### Answer: 10 hours
Expected answer: 10
Correct? Yes
Problem: Suppose there are more guards available and Captain Blackbeard decided to split the total time into 12 shifts instead of 6. How many hours will each guard now have to protect the ship under this new arrangement?
GPT-4o:
To determine how many hours each guard will have to protect the ship under the new arrangement, we need to divide the total number of hours by the new number of shifts. Total hours sailed: 60 hours New number of shifts: 12 We perform the division: \[ \frac{60 \text{ hours}}{12 \text{ shifts}} = 5 \text{ hours per shift} \] Thus, each guard will now have to protect the ship for 5 hours. ### Answer: 5 hours
Expected answer: 5
Correct? Yes
Problem: John needs a rope. Every meter of the rope costs $5. If John needs a 6-meter long rope, how much will it cost him?
GPT-4o:
To determine the total cost of the rope, we need to multiply the cost per meter by the length of the rope John needs. Given: - Cost per meter of rope = $5 - Length of rope needed = 6 meters We calculate the total cost as follows: \[ \text{Total cost} = \text{Cost per meter} \times \text{Length of rope} \] \[ \text{Total cost} = 5 \, \text{dollars/meter} \times 6 \, \text{meters} \] \[ \text{Total cost} = 30 \, \text{dollars} \] ### Answer: $30
Expected answer: 30
Correct? Yes
Problem: Going further from the previous problem, John now realizes he needs twice as much rope! How much will it cost him to buy 12 meters of rope in all?
GPT-4o:
To determine the total cost for 12 meters of rope, we need to multiply the cost per meter by the new length of the rope John needs. Given: - Cost per meter of rope = $5 - New length of rope needed = 12 meters We calculate the total cost as follows: \[ \text{Total cost} = \text{Cost per meter} \times \text{Length of rope} \] \[ \text{Total cost} = 5 \, \text{dollars/meter} \times 12 \, \text{meters} \] \[ \text{Total cost} = 60 \, \text{dollars} \] ### Answer: $60
Expected answer: 60
Correct? Yes
Problem: After considering his needs again, John realized that he actually needs 7 meters of rope, not 6. How much will it cost him to buy this new length of rope?
GPT-4o:
To determine the new total cost of the rope, we need to multiply the cost per meter by the new length of the rope John needs. Given: - Cost per meter of rope = $5 - New length of rope needed = 7 meters We calculate the total cost as follows: \[ \text{Total cost} = \text{Cost per meter} \times \text{Length of rope} \] \[ \text{Total cost} = 5 \, \text{dollars/meter} \times 7 \, \text{meters} \] \[ \text{Total cost} = 35 \, \text{dollars} \] ### Answer: $35
Expected answer: 35
Correct? Yes
Problem: Amelia has 42 gifts to distribute equally among her 7 best friends. How many gifts will each friend receive?
GPT-4o:
To determine how many gifts each of Amelia's friends will receive, we need to divide the total number of gifts by the number of friends. Given: - Total number of gifts = 42 - Number of friends = 7 We perform the division: \[ \frac{42}{7} = 6 \] So, each friend will receive 6 gifts. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: In the previous scenario, Amelia was distributing gifts among 7 of her friends. But what if Amelia instead planned to distribute her 42 gifts equally among only 6 friends instead? How many gifts would each friend receive in this case?
GPT-4o:
To determine how many gifts each of Amelia's friends will receive if she distributes the 42 gifts among 6 friends, we need to divide the total number of gifts by the number of friends. Given: - Total number of gifts = 42 - Number of friends = 6 We perform the division: \[ \frac{42}{6} = 7 \] So, each friend will receive 7 gifts. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: A mother bear has 40 honey pots and she wants to evenly distribute them among her 8 cubs. How many honey pots will each cub receive?
GPT-4o:
To determine how many honey pots each cub will receive, we need to divide the total number of honey pots by the number of cubs. Given: - Total honey pots = 40 - Number of cubs = 8 We perform the division: \[ \frac{40}{8} = 5 \] So, each cub will receive 5 honey pots. ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: If the mother bear had only 40 honey pots and wanted to evenly distribute them among her 10 cubs instead, how many honey pots would each cub receive now?
GPT-4o:
To determine how many honey pots each cub will receive if the mother bear distributes them among 10 cubs, we need to divide the total number of honey pots by the number of cubs. Given: - Total honey pots = 40 - Number of cubs = 10 We perform the division: \[ \frac{40}{10} = 4 \] So, each cub will receive 4 honey pots. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: A penguin is diving into the sea. Initially, it took the penguin 28 seconds to reach a depth that is 4 times its own height. What is the square of the depth the penguin reaches in seconds?
GPT-4o:
To solve this problem, we need to determine the depth the penguin reaches and then find the square of that depth. First, let's denote the penguin's height as \( h \). According to the problem, the depth the penguin reaches is 4 times its height, which can be expressed as \( 4h \). Next, we are given that it took the penguin 28 seconds to reach this depth. However, the problem asks for the square of the depth in seconds, not the time taken. The depth the penguin reaches is \( 4h \). To find the square of this depth, we calculate: \[ (4h)^2 = 16h^2 \] Since the problem does not provide the actual height \( h \) of the penguin, we can only express the square of the depth in terms of \( h \). ### Answer: 16h^2
Expected answer: 49
Correct? No
Problem: A swing goes back and forth 10 times every minute. How many back and forth swings will the swing accomplish in 9 minutes?
GPT-4o:
To determine the total number of back and forth swings the swing will accomplish in 9 minutes, we start by noting that the swing goes back and forth 10 times every minute. First, we calculate the number of swings per minute: \[ 10 \text{ swings/minute} \] Next, we multiply the number of swings per minute by the total number of minutes: \[ 10 \text{ swings/minute} \times 9 \text{ minutes} = 90 \text{ swings} \] Thus, the swing will accomplish 90 back and forth swings in 9 minutes. ### Answer: 90
Expected answer: 90
Correct? Yes
Problem: An elephant can eat 7kg food per hour. How much food will an elephant eat in 4 hours?
GPT-4o:
To determine how much food an elephant will eat in 4 hours, we need to multiply the amount of food it eats per hour by the number of hours. Given: - The elephant eats 7 kg of food per hour. - The time period is 4 hours. Calculation: \[ 7 \, \text{kg/hour} \times 4 \, \text{hours} = 28 \, \text{kg} \] ### Answer: 28 kg
Expected answer: 28
Correct? Yes
Problem: In the previous situation, what if instead of eating 4kg of food per hour, the elephant ate only 3kg of food per hour? How much food would the elephant eat in 4 hours then?
GPT-4o:
To determine how much food the elephant will eat in 4 hours if it eats 3 kg of food per hour, we need to multiply the amount of food it eats per hour by the number of hours. Given: - The elephant eats 3 kg of food per hour. - The time period is 4 hours. Calculation: \[ 3 \, \text{kg/hour} \times 4 \, \text{hours} = 12 \, \text{kg} \] ### Answer: 12 kg
Expected answer: 12
Correct? Yes
Problem: A dragon has 3 heads and each head has 8 eyes. How many eyes does the dragon have in total?
GPT-4o:
To determine the total number of eyes the dragon has, we need to multiply the number of heads by the number of eyes per head. The dragon has 3 heads, and each head has 8 eyes. Therefore, we calculate: \[ 3 \text{ heads} \times 8 \text{ eyes per head} = 24 \text{ eyes} \] ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: In addition to the 3-headed dragon, another dragon of the same kind joins it. Between the two dragons, how many eyes are there in total?
GPT-4o:
We already know that one dragon has 24 eyes. Since another dragon of the same kind joins it, we need to calculate the total number of eyes for both dragons. Each dragon has 24 eyes, so for two dragons, we calculate: \[ 24 \text{ eyes per dragon} \times 2 \text{ dragons} = 48 \text{ eyes} \] ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: Suppose that each dragon instead had 11 eyes per head, not 8. How many eyes would one three-headed dragon have then?
GPT-4o:
To find the total number of eyes for a three-headed dragon where each head has 11 eyes, we multiply the number of heads by the number of eyes per head. The dragon has 3 heads, and each head has 11 eyes. Therefore, we calculate: \[ 3 \text{ heads} \times 11 \text{ eyes per head} = 33 \text{ eyes} \] ### Answer: 33
Expected answer: 33
Correct? Yes
Problem: A candle burns out at a rate of 2 hours per inch. If a candle is 3 inches tall, how long will it take for the candle to burn out completely?
GPT-4o:
To determine how long it will take for the candle to burn out completely, we need to multiply the height of the candle by the rate at which it burns. The candle is 3 inches tall, and it burns at a rate of 2 hours per inch. So, the total time to burn out the candle is: \[ 3 \text{ inches} \times 2 \text{ hours per inch} = 6 \text{ hours} \] ### Answer: 6 hours
Expected answer: 6
Correct? Yes
Problem: Charlie has 4 chocolates and decides to share half of them with his sister. Then he counts his remaining chocolates and decides to double the amount. How many chocolates does Charlie have now?
GPT-4o:
First, let's determine how many chocolates Charlie shares with his sister. He has 4 chocolates and decides to share half of them: \[ \frac{4}{2} = 2 \] So, Charlie shares 2 chocolates with his sister. This leaves him with: \[ 4 - 2 = 2 \] Next, Charlie decides to double the amount of chocolates he has left: \[ 2 \times 2 = 4 \] Therefore, after sharing and then doubling, Charlie has: ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: Following from the last problem, Charlie then takes the amount of chocolates he has and decides to multiply it by 9 for a birthday party. How many chocolates does Charlie have now?
GPT-4o:
From the previous problem, we know that Charlie has 4 chocolates. He decides to multiply this amount by 9 for a birthday party. \[ 4 \times 9 = 36 \] Therefore, after multiplying by 9, Charlie has: ### Answer: 36
Expected answer: 36
Correct? Yes
Problem: Following from the previous problems, let's consider a new scenario. This time, suppose Charlie only had 2 chocolates and again decided to share half of them with his sister. Then, he counts his remaining chocolates and decides to double the amount. How many chocolates does Charlie have now in this scenario?
GPT-4o:
First, let's determine how many chocolates Charlie shares with his sister. He has 2 chocolates and decides to share half of them: \[ \frac{2}{2} = 1 \] So, Charlie shares 1 chocolate with his sister. This leaves him with: \[ 2 - 1 = 1 \] Next, Charlie decides to double the amount of chocolates he has left: \[ 1 \times 2 = 2 \] Therefore, after sharing and then doubling, Charlie has: ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: A castle has 36 towers and there are an equal number of towers on each of its 6 walls. How many towers are there on each wall?
GPT-4o:
To determine the number of towers on each wall, we need to divide the total number of towers by the number of walls. Given: - Total number of towers = 36 - Number of walls = 6 We perform the division: \[ \frac{36}{6} = 6 \] So, there are 6 towers on each wall. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: Suppose the number of walls in the castle was incorrectly counted before, and there are actually 10 walls instead of 6. If the castle still has a total of 36 towers, how many towers would be on each wall in that case?
GPT-4o:
To find the number of towers on each wall with the updated number of walls, we need to divide the total number of towers by the new number of walls. Given: - Total number of towers = 36 - Number of walls = 10 We perform the division: \[ \frac{36}{10} = 3.6 \] So, there would be 3.6 towers on each wall. ### Answer: 3.6
Expected answer: 18/5
Correct? Yes