Datasets:
aishitdharwal
/
math-dataset

Dataset card Data Studio Files
xet
Community
1
example
stringlengths
183
3.89k
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Younghee, Jimin, and Junsu had a water drinking contest for two days. Younghee drank 1.4 liters (L), Jimin drank 1.8 liters (L), and Junsu drank 2.1 liters (L). Who is the winner? [/INST] Junsu is the winner of the water drinking contest, as he drank the most water with a total of 2.1 liters (L).</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. There were 82 people on the train. A few of these got off, and 17 more got on, making the total 73 people. How many people got off the train? [/INST] Let's call the number of people who got off the train x. Initially, there were 82 people on the train. After x people got off, there were 82 - x people left on the train. Then, 17 more people got on, making the total number of people on the train 82 - x + 17. We are told that this total is 73 people. So we can set up the following equation: 82 - x + 17 = 73 Now, let's solve for x: 82 - x + 17 = 73 82 + 17 - x = 73 99 - x = 73 -x = 73 - 99 -x = -26 To find x, we multiply both sides by -1: x = 26 So, 26 people got off the train.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. A cuboid space can contain 36 boxes, each measuring 1 centimeter (cm) in length, width, and height. How many boxes could fit in this space if you double its length, width, and height? [/INST] If the original cuboid space can contain 36 boxes, each measuring 1 cm in length, width, and height, then the volume of the original space is 36 cubic centimeters (since each box is 1 cm³). If you double the length, width, and height of the cuboid space, the new dimensions will be 2 times the original dimensions. Let's assume the original dimensions of the cuboid space are L cm in length, W cm in width, and H cm in height. The volume of the original space is L * W * H = 36 cm³. When you double each dimension, the new length is 2L, the new width is 2W, and the new height is 2H. The volume of the new space is (2L) * (2W) * (2H). The new volume is 2^3 times the original volume because you have doubled each of the three dimensions. So the new volume is 2^3 * 36 cm³ = 8 * 36 cm³ = 288 cm³. Therefore, if you double the length, width, and height of the original space, you can fit 288 boxes, each measuring 1 cm in length, width, and height.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. There are 36 students in Jaehong's class. If there are 24 fewer students wearing short sleeves than students wearing long sleeves, find how many students are wearing short sleeves. [/INST] Let's denote the number of students wearing short sleeves as S and the number of students wearing long sleeves as L. According to the problem, we have two pieces of information: 1. The total number of students in the class is 36. 2. There are 24 fewer students wearing short sleeves than students wearing long sleeves. We can express these two pieces of information as equations: 1. S + L = 36 (since the total number of students is the sum of those wearing short sleeves and those wearing long sleeves) 2. L - S = 24 (since there are 24 fewer students wearing short sleeves than those wearing long sleeves) Now we have a system of two equations with two variables. We can solve this system by adding the two equations together to eliminate one of the variables: S + L = 36 L - S = 24 ----------- 2L = 60 Now, divide both sides by 2 to solve for L: 2L / 2 = 60 / 2 L = 30 Now that we know there are 30 students wearing long sleeves, we can use either of the original equations to find the number of students wearing short sleeves. Let's use the first equation: S + L = 36 S + 30 = 36 S = 36 - 30 S = 6 So, there are 6 students wearing short sleeves in Jaehong's class.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. A box of apples weighed 9 kilograms (kg). After removing half of the apples, I weighed it again and it was 5 kilograms (kg). If each apple is the same size and weight, how many kilograms (kg) does only one box except apples weigh? [/INST] Initially, the box with all the apples weighed 9 kg. After removing half of the apples, the box weighed 5 kg. The difference in weight, which is 4 kg, is due to the weight of half of the apples that were removed. Since this 4 kg is half the weight of all the apples, the total weight of all the apples when the box was full would be 4 kg * 2 = 8 kg. Now, to find the weight of the box without any apples, we subtract the weight of all the apples from the initial total weight: 9 kg (initial weight with all apples) - 8 kg (weight of all apples) = 1 kg. Therefore, the weight of the box without any apples is 1 kg.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Jiseok's backpack weighs 1.49 kilograms (kg), and Miho's backpack weighs 9/20 kilograms (kg). What is the name of the person whose backpack weighs less? [/INST] Miho's backpack weighs 9/20 kilograms, which is equivalent to 0.45 kilograms (since 9 divided by 20 equals 0.45). Since 0.45 kg is less than 1.49 kg, Miho's backpack weighs less. Therefore, the name of the person whose backpack weighs less is Miho.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Youngbin and Sujeong had a competition to pick up coins faster. If it took Yeongbin 16.23 seconds and Sujeong 16.19 seconds to pick up all the coins, who wins? [/INST] Sujeong wins the competition because she took less time, 16.19 seconds, compared to Youngbin's 16.23 seconds to pick up all the coins.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. When you divide 48 by a number and add 7 to the quotient of it, you get 15. Figure out what the number is. [/INST] Let's call the number you're dividing by "x". According to the problem, when you divide 48 by x and add 7, you get 15. We can set up the following equation to represent this: 48/x + 7 = 15 Now, we want to solve for x. First, we'll subtract 7 from both sides of the equation to isolate the division part: 48/x = 15 - 7 48/x = 8 Now, to solve for x, we'll multiply both sides of the equation by x and then divide both sides by 8: 48 = 8x 48/8 = x 6 = x So the number you're dividing by is 6.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. When two of the number cards 4, 3, and 1 are used once to form the largest two-digit number, what is the number on the unused card? [/INST] To form the largest two-digit number using two of the cards 4, 3, and 1, we should place the largest digit in the tens place and the second largest digit in the ones place. The largest digit among 4, 3, and 1 is 4, and the second largest is 3. So, the largest two-digit number we can form is 43. The unused card is the one with the number 1 on it.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Students stand in a line. Yoojung is standing on the far right. Eunjeong is standing 5th from the far left. When 8 students are standing between Eunjeong and Yoojung, how many students are in line? [/INST] Let's break down the information given: 1. Yoojung is standing on the far right. 2. Eunjeong is standing 5th from the far left. 3. There are 8 students standing between Eunjeong and Yoojung. To find out the total number of students in line, we need to add up all the positions: - The 4 students to the left of Eunjeong (since Eunjeong is the 5th from the left, we don't count her in these 4). - Eunjeong herself. - The 8 students between Eunjeong and Yoojung. - Yoojung, who is on the far right. So, the total number of students is: 4 (to the left of Eunjeong) + 1 (Eunjeong) + 8 (between Eunjeong and Yoojung) + 1 (Yoojung) = 14 students in line.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. There are 1500 students in Sarang's School, 0.4 of which are female students. If 0.65 of the male students at Sarang's School like math, how many male students do not like math? [/INST] First, let's find out how many female students there are in Sarang's school. Since 0.4 of the students are female, we can calculate the number of female students as follows: Number of female students = Total number of students * Proportion of female students Number of female students = 1500 * 0.4 Number of female students = 600 Now, let's find out how many male students there are. Since the total number of students is 1500 and we have already found out that there are 600 female students, we can subtract the number of female students from the total number of students to get the number of male students: Number of male students = Total number of students - Number of female students Number of male students = 1500 - 600 Number of male students = 900 Now, we know that 0.65 of the male students like math. To find out how many male students do not like math, we first need to find out how many male students like math and then subtract that number from the total number of male students. Number of male students who like math = Number of male students * Proportion of male students who like math Number of male students who like math = 900 * 0.65 Number of male students who like math = 585 Now, we can find out how many male students do not like math by subtracting the number of male students who like math from the total number of male students: Number of male students who do not like math = Number of male students - Number of male students who like math Number of male students who do not like math = 900 - 585 Number of male students who do not like math = 315 Therefore, there are 315 male students at Sarang's school who do not like math.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. The width and height of a rectangle with an area of 32 are both natural numbers. Find the number of possible rectangles. (However, when the width and height are swapped, the same rectangle is considered identical.) [/INST] To find the number of possible rectangles with an area of 32 where the width and height are natural numbers (positive integers), we need to find all the pairs of factors of 32. Since swapping width and height results in the same rectangle, we only count distinct pairs once. The factors of 32 are: 1, 2, 4, 8, 16, 32. Now, we can pair these factors to get the area of 32: 1. (1, 32) 2. (2, 16) 3. (4, 8) We do not consider (8, 4), (16, 2), or (32, 1) as they are the same rectangles as the ones already listed, just with the dimensions swapped. Therefore, there are 3 possible rectangles with an area of 32 where the width and height are natural numbers and the rectangles are considered identical when the dimensions are swapped.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. If A is the number of diagonals in a heptagon and B is the number of diagonals in an octagon, find the value of B-A. [/INST] The formula to find the number of diagonals in a polygon with n sides is given by: Number of diagonals = n(n - 3)/2 For a heptagon (7 sides), let's find A: A = 7(7 - 3)/2 A = 7(4)/2 A = 28/2 A = 14 For an octagon (8 sides), let's find B: B = 8(8 - 3)/2 B = 8(5)/2 B = 40/2 B = 20 Now, let's find B - A: B - A = 20 - 14 B - A = 6 Therefore, the value of B - A is 6.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Sooae and Seungho had a 100 meters (m) running race. If Sooae took 16.23 seconds and Seungho took 16.19 seconds to run 100 meters (m), who ran faster? [/INST] Seungho ran faster because he took less time to complete the 100 meters. Seungho finished the race in 16.19 seconds, while Sooae finished in 16.23 seconds. Since a shorter time indicates a faster speed in a race, Seungho was the faster runner.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. There are 156 dureums of gulbis. How many gulbis are there in all? (One dureum equals 20 fish) [/INST] If one dureum equals 20 fish, then to find the total number of gulbis, you would multiply the number of dureums by the number of fish in one dureum. 156 dureums * 20 fish/dureum = 3120 fish So, there are 3120 gulbis in all.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. There are 2 bars of different lengths. The length of the long stick is 12 centimeters (cm) longer than the length of the short stick, and the sum of the lengths of the two sticks is 20 centimeters (cm). Find how many sticks the same length as the shorter sticks can be made by cutting the longer sticks. [/INST] Let's denote the length of the short stick as \( S \) cm. According to the problem, the length of the long stick is \( S + 12 \) cm. We are also told that the sum of the lengths of the two sticks is 20 cm. Therefore, we can write the following equation: \[ S + (S + 12) = 20 \] Now, let's solve for \( S \): \[ 2S + 12 = 20 \] \[ 2S = 20 - 12 \] \[ 2S = 8 \] \[ S = \frac{8}{2} \] \[ S = 4 \] So, the length of the short stick is 4 cm. Now, let's find the length of the long stick: \[ S + 12 = 4 + 12 = 16 \] The long stick is 16 cm long. To find out how many sticks the same length as the shorter sticks can be made by cutting the longer sticks, we divide the length of the long stick by the length of the short stick: \[ \frac{16}{4} = 4 \] Therefore, 4 sticks the same length as the shorter sticks can be made by cutting the longer stick.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. The proportion of blue tulips is 3/8 of the 56 tulips. If 3/7 of the total are red tulips, and the others pink, how many pink tulips are there? [/INST] First, let's find out how many blue tulips there are. Since the proportion of blue tulips is 3/8 of the total 56 tulips, we can calculate the number of blue tulips as follows: Number of blue tulips = (3/8) * 56 Now, let's find out how many red tulips there are. Since 3/7 of the total tulips are red, we can calculate the number of red tulips as follows: Number of red tulips = (3/7) * 56 After finding the number of blue and red tulips, we can subtract their sum from the total number of tulips to find out how many pink tulips there are. Number of pink tulips = Total number of tulips - (Number of blue tulips + Number of red tulips) Let's do the calculations: Number of blue tulips = (3/8) * 56 = 3 * 7 = 21 Number of red tulips = (3/7) * 56 = 3 * 8 = 24 Number of pink tulips = 56 - (21 + 24) = 56 - 45 = 11 So, there are 11 pink tulips.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Jungwoo drew a rectangle and a square with the same area during drawing time. The two sides of the rectangle drawn by JungWoo are 9 centimeters (cm) and 16 centimeters (cm), respectively. How many centimeters (cm) is the length of one side of the square? [/INST] To find the length of one side of the square, we first need to calculate the area of the rectangle. The area of a rectangle is found by multiplying the length of one side by the length of the adjacent side. For Jungwoo's rectangle, the sides are 9 cm and 16 cm, so the area is: Area = length × width Area = 9 cm × 16 cm Area = 144 cm² Since the square has the same area as the rectangle, the area of the square is also 144 cm². The area of a square is found by squaring the length of one of its sides (since all sides of a square are equal in length). Let's call the length of the side of the square 's'. Area of square = s² We know the area is 144 cm², so: s² = 144 cm² To find the length of the side 's', we take the square root of the area: s = √144 cm² s = 12 cm Therefore, the length of one side of the square is 12 centimeters.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Using the four number cards 0, 1, 4, and 8 once, find the number of three-digit numbers where the tens digit is zero. [/INST] To form a three-digit number with the tens digit as zero, we need to place the '0' in the tens place. This leaves us with the hundreds and units places to fill with the remaining three numbers: 1, 4, and 8. For the hundreds place, we can choose any of the three remaining numbers (1, 4, or 8). Once we choose a number for the hundreds place, we have two numbers left for the units place. So, the number of three-digit numbers we can form with the tens digit as zero is the number of choices for the hundreds place multiplied by the number of choices for the units place. Number of choices for hundreds place = 3 (1, 4, or 8) Number of choices for units place = 2 (the remaining two numbers after choosing the hundreds place) Therefore, the total number of three-digit numbers we can form is: 3 (choices for hundreds place) * 2 (choices for units place) = 6 So, there are 6 possible three-digit numbers where the tens digit is zero using the numbers 0, 1, 4, and 8 once.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. There are 5 bottles that each contains 242.7 milliliters (ml) of beverage. How many milliliters (ml) of beverage are there? [/INST] To find the total amount of beverage in milliliters, you need to multiply the amount in one bottle by the number of bottles. So, 242.7 ml/bottle * 5 bottles = 1213.5 ml There are 1213.5 milliliters of beverage in total.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. 20 students stood in a line. Jungkook stood in third place, and Yoongi stood right in front of Jungkook. How many students are standing behind Yoongi? [/INST] If Jungkook stood in third place, that means there are two students in front of him. Since Yoongi stood right in front of Jungkook, Yoongi is the second student in line. Therefore, there are 20 - 2 = 18 students standing behind Yoongi.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Yoongi is 2 years younger than Hoseok, and together, Yoongi and Hoseok are 18 years old. How old is Yoongi? [/INST] Let's denote Yoongi's age as Y and Hoseok's age as H. According to the information given: 1) Yoongi is 2 years younger than Hoseok, so we can write this as: Y = H - 2 2) Together, their ages add up to 18 years, so we can write this as: Y + H = 18 Now we can substitute the first equation into the second equation to solve for Y: (Y) + (Y + 2) = 18 2Y + 2 = 18 2Y = 18 - 2 2Y = 16 Y = 16 / 2 Y = 8 So, Yoongi is 8 years old.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. There are 23 fewer basketballs at Hoseok's school than soccer balls, and 18 more soccer balls than volleyballs. If there are 40 volleyballs, how many basketballs are there? [/INST] Let's start by figuring out how many soccer balls there are. Since there are 18 more soccer balls than volleyballs and there are 40 volleyballs, we can calculate the number of soccer balls as follows: Number of soccer balls = Number of volleyballs + 18 Number of soccer balls = 40 + 18 Number of soccer balls = 58 Now, we know there are 23 fewer basketballs than soccer balls. So, we can calculate the number of basketballs as follows: Number of basketballs = Number of soccer balls - 23 Number of basketballs = 58 - 23 Number of basketballs = 35 Therefore, there are 35 basketballs at Hoseok's school.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. It is said that four times the number of persimmons Jungkook picked equals the number minus three persimmons picked by Hoseok. When Hoseok picked 35 persimmons, how many persimmons did Jungkook pick? [/INST] Let's denote the number of persimmons Jungkook picked as \( J \) and the number of persimmons Hoseok picked as \( H \). According to the problem, we have the following equation: \[ 4J = H - 3 \] We are given that Hoseok picked 35 persimmons, so \( H = 35 \). Now we can substitute \( H \) into the equation: \[ 4J = 35 - 3 \] Simplify the right side of the equation: \[ 4J = 32 \] Now, to find the number of persimmons Jungkook picked (\( J \)), we divide both sides of the equation by 4: \[ J = \frac{32}{4} \] \[ J = 8 \] So, Jungkook picked 8 persimmons.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. If Dong-min stands on a chair with a height of 53 centimeters (cm) 7 millimeters (mm) and measures his height from the floor, he will be 190 centimeters (cm), and if he stands on a desk and measures his height from the floor, he will be 232 centimeters (cm) and 5 millimeters (mm). How tall is the desk? [/INST] First, let's find out Dong-min's actual height without standing on anything. We know that when he stands on the chair, he measures 190 cm from the floor. The chair is 53 cm 7 mm tall. To find Dong-min's height, we need to subtract the height of the chair from the total height measured when he is standing on the chair. Since we are working with centimeters and millimeters, we need to convert the measurements to the same unit. There are 10 millimeters in a centimeter, so 53 cm 7 mm is the same as 530 mm + 7 mm = 537 mm. Now, let's convert Dong-min's height when standing on the chair to millimeters as well: 190 cm = 1900 mm Now we subtract the height of the chair in millimeters from Dong-min's total height in millimeters when standing on the chair: 1900 mm - 537 mm = 1363 mm So, Dong-min's height is 1363 mm. Now let's convert this back to centimeters: 1363 mm = 136 cm 3 mm Now we need to find out the height of the desk. When Dong-min stands on the desk, he measures 232 cm 5 mm from the floor. Let's convert this to millimeters: 232 cm 5 mm = 2320 mm + 5 mm = 2325 mm Now we subtract Dong-min's height in millimeters from the total height measured when he is standing on the desk: 2325 mm - 1363 mm = 962 mm So, the desk is 962 mm tall. Converting this back to centimeters and millimeters: 962 mm = 96 cm 2 mm Therefore, the desk is 96 centimeters and 2 millimeters tall.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Find the sum of the largest and smallest two-digit numbers that can be formed by drawing two different numbers from 0, 3, 5, 7, and 8. [/INST] To find the largest two-digit number, we need to select the largest available digits for the tens and ones places. From the given digits 0, 3, 5, 7, and 8, the largest digit is 8 and the second largest is 7. However, we cannot use 0 as the tens digit because that would not make a two-digit number. Therefore, the largest two-digit number we can form is 87. To find the smallest two-digit number, we need to select the smallest non-zero digit for the tens place and the smallest digit for the ones place. The smallest non-zero digit available is 3, and the next smallest digit we can use for the ones place is 0. Therefore, the smallest two-digit number we can form is 30. Now, we find the sum of the largest and smallest two-digit numbers: 87 (largest two-digit number) + 30 (smallest two-digit number) = 117 So, the sum of the largest and smallest two-digit numbers that can be formed by drawing two different numbers from 0, 3, 5, 7, and 8 is 117.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Jinseok's backpack weighs 1.49 kilograms (kg) and Miho's backpack weighs 9/20 kilograms (kg). Whose backpack is lighter? [/INST] To compare the weights of Jinseok's and Miho's backpacks, we need to ensure that both weights are in the same units. They are both in kilograms, so we can compare them directly. Jinseok's backpack weighs 1.49 kg. Miho's backpack weighs 9/20 kg. To convert this fraction to a decimal, we divide the numerator by the denominator: 9 ÷ 20 = 0.45 kg Now we can compare the two weights: Jinseok's backpack: 1.49 kg Miho's backpack: 0.45 kg Since 0.45 kg is less than 1.49 kg, Miho's backpack is lighter.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. The sum of 4 consecutive odd numbers is 112. Write down the 2nd smallest of these 4 numbers. [/INST] Let's denote the smallest of the four consecutive odd numbers as \( n \). Since odd numbers are separated by a difference of 2, the next three consecutive odd numbers would be \( n+2 \), \( n+4 \), and \( n+6 \). According to the problem, the sum of these four consecutive odd numbers is 112: \[ n + (n+2) + (n+4) + (n+6) = 112 \] Combining like terms, we get: \[ 4n + 12 = 112 \] Subtract 12 from both sides: \[ 4n = 100 \] Divide both sides by 4: \[ n = 25 \] So the smallest of the four consecutive odd numbers is 25. The second smallest would be the next odd number, which is \( n+2 \): \[ 25 + 2 = 27 \] Therefore, the second smallest of the four consecutive odd numbers is 27.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. When Daehyeon and Donggil cleaned the school for 8 days, an area equivalent to 7/12 of the total area was cleaned. If it took 10 days for Daehyeon to clean the rest of the area by himself, how many days did it take for Donggil to clean the entire area alone? [/INST] Let's denote the total area of the school as A. According to the information given, Daehyeon and Donggil cleaned 7/12 of the total area in 8 days. This means that the remaining area to be cleaned is 5/12 of A. Let's denote the rate at which Daehyeon cleans as D (area per day) and the rate at which Donggil cleans as G (area per day). When they work together, their combined rate is D + G. From the information given, we can write the following equation for the work done by both of them together in 8 days: (D + G) * 8 = 7/12 * A Now, it took Daehyeon 10 days to clean the remaining 5/12 of the area by himself. This gives us another equation: D * 10 = 5/12 * A From the second equation, we can solve for D: D = (5/12 * A) / 10 D = 5/120 * A D = 1/24 * A Now, let's substitute D back into the first equation to solve for G: (D + G) * 8 = 7/12 * A (1/24 * A + G) * 8 = 7/12 * A 8/24 * A + 8G = 7/12 * A 1/3 * A + 8G = 7/12 * A Now, let's solve for G: 8G = 7/12 * A - 1/3 * A 8G = 7/12 * A - 4/12 * A 8G = 3/12 * A 8G = 1/4 * A G = (1/4 * A) / 8 G = 1/32 * A Now we know the rate at which Donggil cleans the area by himself. To find out how many days it would take for Donggil to clean the entire area alone, we use the following equation: G * days = A Substituting G into the equation: (1/32 * A) * days = A To find the number of days, we divide both sides by (1/32 * A): days = A / (1/32 * A) days = 32 Therefore, it would take Donggil 32 days to clean the entire area of the school by himself.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. A number equals a number minus 5 and multiply it by 4. Find some number. [/INST] Let's call the number we're trying to find "n". According to the statement, the number equals itself minus 5, and then multiplied by 4. We can set up the following equation: n = (n - 5) * 4 Now, let's solve for n: n = 4n - 20 To solve for n, we need to get all the n terms on one side of the equation. Let's move the 4n to the left side by subtracting 4n from both sides: n - 4n = -20 This simplifies to: -3n = -20 Now, divide both sides by -3 to solve for n: n = -20 / -3 n = 20 / 3 n = 6.666... So, the number is 6.666..., or as a fraction, 20/3.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. When the three numbers 1, 2, and 3 are used repeatedly to form a four-digit number, how many ways can the sum be 10? [/INST] To form a four-digit number using the numbers 1, 2, and 3 repeatedly, and to have the sum of the digits be 10, we need to find all the combinations of 1, 2, and 3 that add up to 10 when four digits are used. Let's denote the four digits as A, B, C, and D, where each can be 1, 2, or 3. We want A + B + C + D = 10. Here are the possible combinations: 1. 1 + 3 + 3 + 3 = 10 2. 3 + 1 + 3 + 3 = 10 3. 3 + 3 + 1 + 3 = 10 4. 3 + 3 + 3 + 1 = 10 5. 2 + 2 + 3 + 3 = 10 6. 2 + 3 + 2 + 3 = 10 7. 2 + 3 + 3 + 2 = 10 8. 3 + 2 + 2 + 3 = 10 9. 3 + 2 + 3 + 2 = 10 10. 3 + 3 + 2 + 2 = 10 Each combination represents a different way to arrange the digits to sum to 10. Since the order of the digits matters (as we are forming a four-digit number), we have to consider each arrangement as unique. Therefore, there are 10 ways to form a four-digit number using the digits 1, 2, and 3 repeatedly such that the sum of the digits is 10.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. My mother buys the same amount of eggs every month. There were 27 eggs left last month, but since my mother bought eggs, the number has increased to 58. If you eat 48 eggs this month and your mother buys eggs for the next month, how many eggs will there be? [/INST] First, let's find out how many eggs your mother buys each month. We know that there were 27 eggs left last month, and after she bought more, the total increased to 58 eggs. To find out how many eggs she bought, we subtract the number of eggs left from the total number of eggs after she bought more: 58 eggs (after buying) - 27 eggs (left from last month) = 31 eggs bought Now, if you eat 48 eggs this month, we need to subtract that from the current total to find out how many will be left before your mother buys more: 58 eggs (current total) - 48 eggs (eaten this month) = 10 eggs left Since we know your mother buys 31 eggs each month, we add that to the number of eggs left to find out how many eggs there will be after she buys more for the next month: 10 eggs (left) + 31 eggs (bought) = 41 eggs So, there will be 41 eggs after your mother buys eggs for the next month.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. How many cubic meters (m3) is the volume of a rectangular parallelepiped made by doubling the length, width, and height of a rectangular parallelepiped with a width of 80 centimeters (cm), a length of 75 centimeters (cm), and a height of 120 centimeters (cm)? Save it. [/INST] First, let's find the volume of the original rectangular parallelepiped: Volume = Length × Width × Height Given the original dimensions in centimeters: Length (L) = 75 cm Width (W) = 80 cm Height (H) = 120 cm Volume_original = L × W × H Volume_original = 75 cm × 80 cm × 120 cm Volume_original = 720,000 cm³ Now, if we double the length, width, and height, the new dimensions will be: New Length (L') = 2 × 75 cm = 150 cm New Width (W') = 2 × 80 cm = 160 cm New Height (H') = 2 × 120 cm = 240 cm Volume_new = L' × W' × H' Volume_new = 150 cm × 160 cm × 240 cm Volume_new = 5,760,000 cm³ To convert cubic centimeters to cubic meters, we use the conversion factor: 1 m³ = 1,000,000 cm³ Volume_new (in m³) = Volume_new (in cm³) / 1,000,000 Volume_new (in m³) = 5,760,000 cm³ / 1,000,000 Volume_new (in m³) = 5.76 m³ The volume of the rectangular parallelepiped after doubling the dimensions is 5.76 cubic meters (m³).</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. In a factory, machine A makes 8 toys per minute, and machine B makes 10 toys per minute. Provided that both machines started making toys at the same time and machine B made 100 toys, find how many fewer toys machine A made than machine B. [/INST] First, we need to determine how long machine B took to make 100 toys. Since machine B makes 10 toys per minute, we can calculate the time it took for machine B to make 100 toys by dividing the total number of toys by the rate of production: Time for machine B = Total toys made by machine B / Rate of production by machine B Time for machine B = 100 toys / 10 toys per minute Time for machine B = 10 minutes Now that we know machine B took 10 minutes to make 100 toys, we can calculate how many toys machine A made in the same amount of time. Machine A makes 8 toys per minute, so in 10 minutes, machine A would have made: Toys made by machine A = Rate of production by machine A * Time Toys made by machine A = 8 toys per minute * 10 minutes Toys made by machine A = 80 toys Now we can find out how many fewer toys machine A made than machine B by subtracting the number of toys made by machine A from the number of toys made by machine B: Fewer toys made by machine A = Toys made by machine B - Toys made by machine A Fewer toys made by machine A = 100 toys - 80 toys Fewer toys made by machine A = 20 toys Machine A made 20 fewer toys than machine B.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Gayoung has a cube-shaped box with one corner measuring 20 centimeters (cm). What is the surface area of this box? [/INST] If the box is cube-shaped and one corner measures 20 centimeters, this means that each edge of the cube is 20 centimeters long. A cube has 6 faces, and the surface area of each face is the square of the length of one side. So, the surface area of one face is: 20 cm * 20 cm = 400 cm² Since there are 6 faces on a cube, the total surface area of the cube is: 6 * 400 cm² = 2400 cm² Therefore, the surface area of the box is 2400 square centimeters.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. The length of board A is 2.4 centimeters (cm), board B is 3.2 centimeters (cm), and board C is 2.8 centimeters (cm). When Eunji, Namjoon, and Hoseok are standing on top of 8 A boards, 4 B boards, and 5 C boards, respectively, find who is at the lowest. [/INST] To find out who is at the lowest, we need to calculate the total height of the boards each person is standing on. For Eunji standing on 8 A boards: Total height for Eunji = 8 boards * 2.4 cm/board = 19.2 cm For Namjoon standing on 4 B boards: Total height for Namjoon = 4 boards * 3.2 cm/board = 12.8 cm For Hoseok standing on 5 C boards: Total height for Hoseok = 5 boards * 2.8 cm/board = 14 cm Comparing the total heights: Eunji = 19.2 cm Namjoon = 12.8 cm Hoseok = 14 cm Namjoon is at the lowest height since he is standing on boards with a total height of 12.8 cm, which is less than the total height of the boards for Eunji and Hoseok.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. There was a string that was 70 centimeters (cm) long. Of these, 27 centimeters (cm) was given to Minyoung, and 7/9 of the remaining was used to make (A). How many centimeters (cm) is the length of the remaining string? [/INST] First, let's find out how much string was left after giving 27 cm to Minyoung: 70 cm (original length) - 27 cm (given to Minyoung) = 43 cm (remaining) Next, we need to calculate 7/9 of the remaining 43 cm to find out how much was used to make (A): 7/9 * 43 cm = 301/9 cm Now, let's convert the fraction to a decimal to make it easier to understand: 301/9 cm ≈ 33.44 cm (used to make (A)) Finally, we subtract the length used to make (A) from the remaining string to find out the length of the remaining string: 43 cm (remaining after giving to Minyoung) - 33.44 cm (used to make (A)) ≈ 9.56 cm So, the length of the remaining string is approximately 9.56 centimeters.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. You are trying to create a three-digit number using three number cards of 5, 2, and 8 only once. Find the difference between the largest number and the smallest number that can be made. [/INST] To create the largest three-digit number using the digits 5, 2, and 8, you would arrange the digits in descending order: 852. To create the smallest three-digit number using the digits 5, 2, and 8, you would arrange the digits in ascending order: 258. Now, find the difference between the largest and smallest numbers: 852 - 258 = 594 The difference between the largest and smallest three-digit numbers that can be made with the digits 5, 2, and 8 is 594.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. A basket containing 30 pears each weighing 0.36 kilograms (kg) weighs 11.26 kilograms (kg). How many kilograms (kg) does the basket weigh alone? [/INST] To find the weight of the basket alone, we first need to calculate the total weight of the pears. The weight of one pear is 0.36 kg, and there are 30 pears in the basket. So, the total weight of the pears is: 30 pears * 0.36 kg/pear = 10.8 kg Now, we know the total weight of the basket with the pears is 11.26 kg. To find the weight of the basket alone, we subtract the weight of the pears from the total weight: 11.26 kg (total weight) - 10.8 kg (weight of pears) = 0.46 kg Therefore, the basket alone weighs 0.46 kg.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Street trees are to be planted at intervals of 4.5 meters (m) on a road with a length of 63 meters (m). If you plant street trees both at the beginning and at the end, how many trees will you need in total? [/INST] To find out how many trees we will need, we divide the length of the road by the interval at which the trees are to be planted: 63 meters / 4.5 meters = 14 trees However, since we are planting trees at both the beginning and the end of the road, we need to add one more tree to the total count: 14 + 1 = 15 trees So, we will need a total of 15 trees to plant at intervals of 4.5 meters along a 63-meter road, including trees at both the beginning and the end.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. How many centimeters (cm) is the sum of all the side lengths of a regular octagon with a side length of 2.3 meters (m)? [/INST] A regular octagon has 8 sides of equal length. If each side of the octagon is 2.3 meters, we first need to convert the side length from meters to centimeters. There are 100 centimeters in a meter. So, 2.3 meters is equal to 2.3 * 100 centimeters, which is 230 centimeters. Now, to find the sum of all the side lengths of the octagon, we multiply the length of one side by the number of sides (8): 230 cm * 8 = 1840 cm Therefore, the sum of all the side lengths of the regular octagon is 1840 centimeters.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. For the flower arrangement, you will pick one of four roses and one of three tulips and arrange them. When arranging flowers, how many cases are there where you pick only one of the roses and tulips the same? [/INST] To find the number of cases where only one of the roses and tulips is the same, we need to consider the following scenarios: 1. We pick the same rose but different tulips. 2. We pick the same tulip but different roses. Let's calculate each scenario: 1. Same rose, different tulips: Since there are four roses, we can pick any one of them. Then, for the tulips, since we want different tulips, we have 3 choices for the first tulip and 2 choices for the second tulip (since we can't pick the same tulip again). This gives us a total of 4 (roses) * 3 (first tulip choice) * 2 (second tulip choice) = 24 cases. 2. Same tulip, different roses: Similarly, there are three tulips, so we can pick any one of them. For the roses, we have 4 choices for the first rose and 3 choices for the second rose (since we can't pick the same rose again). This gives us a total of 3 (tulips) * 4 (first rose choice) * 3 (second rose choice) = 36 cases. Adding both scenarios together, we get: 24 (same rose, different tulips) + 36 (same tulip, different roses) = 60 cases. Therefore, there are 60 cases where only one of the roses and tulips is the same.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Jinbeom had 12 large and 34 small ttakji. Jinbeom lost several large ttakji and three times as many small ones as he was playing a game of ttakji-chigi. If the number of ttakji Jinbeom currently has is 30, how many large ttakji did Jinbeom lose? [/INST] Let's denote the number of large ttakji Jinbeom lost as L and the number of small ttakji he lost as S. According to the problem, Jinbeom lost three times as many small ttakji as large ones. So we can write: S = 3L Jinbeom originally had 12 large and 34 small ttakji. After losing some, he now has a total of 30 ttakji. So we can write the following equation to represent the total number of ttakji he has left: (12 - L) + (34 - S) = 30 Now we can substitute the value of S from the first equation into the second equation: (12 - L) + (34 - 3L) = 30 Combine like terms: 12 - L + 34 - 3L = 30 46 - 4L = 30 Now, solve for L: 46 - 30 = 4L 16 = 4L L = 16 / 4 L = 4 Jinbeom lost 4 large ttakji.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. You want to plant flags at intervals of 20 meters (m) along a playground track with a circumference of 200 meters (m). If there are 12 flags ready, how many flags are left? Also, if it/s not enough, how many are insufficient? [/INST] To determine how many flags are needed to plant at intervals of 20 meters along a playground track with a circumference of 200 meters, we can divide the total circumference by the interval distance: 200 meters / 20 meters/flag = 10 flags This means you would need 10 flags to place them every 20 meters along the track. Since you have 12 flags ready, we can subtract the number of flags needed from the number you have: 12 flags - 10 flags = 2 flags left Therefore, you will have 2 flags left after placing them along the track. Since you have enough flags (12) and only need 10, there are no insufficient flags. You have more than enough for the task.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. You want to subtract a number from 20. When you mistakenly divide 40 by a number, the result is 5. What is the correct calculation result? [/INST] If dividing 40 by a number gives a result of 5, then the number you divided by is 40/5, which is 8. Now, if you want to subtract this number from 20, the correct calculation would be: 20 - 8 = 12 So the correct result of the calculation is 12.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Find the length of one side of a square whose perimeter is the same as that of a rectangle whose sides are 7 centimeters (cm) long and 5 centimeters (cm) wide. [/INST] First, let's find the perimeter of the rectangle. The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides, the perimeter (P) can be calculated as: P = 2 * (length + width) Given that the length is 7 cm and the width is 5 cm, the perimeter of the rectangle is: P = 2 * (7 cm + 5 cm) P = 2 * 12 cm P = 24 cm Now, we know that the perimeter of the square is the same as the perimeter of the rectangle, which is 24 cm. The perimeter of a square is calculated by adding together the lengths of all four equal sides. Since all sides of a square are equal, the perimeter (P) of a square can also be calculated as: P = 4 * side_length Given that the perimeter of the square is 24 cm, we can find the length of one side (side_length) by dividing the perimeter by 4: side_length = P / 4 side_length = 24 cm / 4 side_length = 6 cm Therefore, the length of one side of the square is 6 cm.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. What is the sum of all numbers greater than or equal to 0.4 among 0.8, 1/2, and 0.9? [/INST] First, let's convert all the numbers to decimals to make it easier to compare and add them: 0.8 is already in decimal form. 1/2 is equal to 0.5 when converted to a decimal. 0.9 is already in decimal form. Now, we need to find all the numbers that are greater than or equal to 0.4: 0.8 is greater than 0.4. 0.5 is greater than 0.4. 0.9 is greater than 0.4. All the numbers are greater than or equal to 0.4, so we will add them all together: 0.8 + 0.5 + 0.9 = 2.2 The sum of all numbers greater than or equal to 0.4 among 0.8, 1/2, and 0.9 is 2.2.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. In the fairy tale Jack and the Beanstalk, there is a scene where Jack climbs the beanstalk. Jack climbs 25 meters (m) during the day and slides down 3 meters (m) at night. If Jack climbed 25 meters (m) during the day on the 64th day and reached the sky island, find the height in meters (m) of the sky island. [/INST] To find the height of the sky island, we need to calculate the total distance Jack climbed over the 64 days, taking into account the sliding down at night. For the first 63 days, Jack climbs 25 meters during the day and slides down 3 meters at night, resulting in a net climb of: 25 meters (climbed) - 3 meters (slid) = 22 meters net climb per day For 63 days, the total net climb would be: 63 days * 22 meters/day = 1386 meters On the 64th day, Jack climbs 25 meters and reaches the sky island without sliding down at night, so we add these 25 meters to the total: 1386 meters + 25 meters = 1411 meters Therefore, the height of the sky island is 1411 meters.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Haeun is 1.56 meters (m) tall. Nayeon is 0.14 meters (m) shorter than Haeun and 0.27 meters (m) shorter than Minkyung. How tall is Minkyung in meters (m)? [/INST] If Nayeon is 0.14 meters shorter than Haeun, we can calculate Nayeon's height by subtracting 0.14 meters from Haeun's height. Haeun's height = 1.56 meters Nayeon's height = Haeun's height - 0.14 meters Nayeon's height = 1.56 meters - 0.14 meters Nayeon's height = 1.42 meters Now, if Nayeon is 0.27 meters shorter than Minkyung, we can calculate Minkyung's height by adding 0.27 meters to Nayeon's height. Minkyung's height = Nayeon's height + 0.27 meters Minkyung's height = 1.42 meters + 0.27 meters Minkyung's height = 1.69 meters Therefore, Minkyung is 1.69 meters tall.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. There are four numbers 0.8, 1/2, 0.9, and 1/3. How many numbers are less than 3? [/INST] All four numbers are less than 3. 0.8 is less than 3. 1/2 (which is 0.5) is less than 3. 0.9 is less than 3. 1/3 (which is approximately 0.333) is less than 3. Therefore, all four numbers are less than 3.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. If there are 6 people A, B, C, D, E, and F, find the number of ways to select 2 subjects and 1 king. [/INST] To solve this problem, we need to consider two separate selections: choosing 2 subjects and choosing 1 king. First, let's find the number of ways to select 2 subjects from the 6 people. This is a combination problem since the order in which we select the subjects does not matter. The formula for combinations is: C(n, k) = n! / (k! * (n - k)!) Where: - n is the total number of items to choose from, - k is the number of items to choose, - "!" denotes factorial, which is the product of all positive integers up to that number. For selecting 2 subjects from 6 people, we have: C(6, 2) = 6! / (2! * (6 - 2)!) C(6, 2) = 6! / (2! * 4!) C(6, 2) = (6 * 5 * 4!) / (2 * 1 * 4!) C(6, 2) = (6 * 5) / (2 * 1) C(6, 2) = 30 / 2 C(6, 2) = 15 So, there are 15 ways to select 2 subjects from 6 people. Next, we need to select 1 king from the remaining 4 people (since 2 have already been chosen as subjects). This is a simple selection problem, and there are 4 ways to choose 1 king from 4 people. Finally, to find the total number of ways to select 2 subjects and 1 king, we multiply the number of ways to select the subjects by the number of ways to select the king: Total ways = Ways to select subjects * Ways to select king Total ways = 15 * 4 Total ways = 60 Therefore, there are 60 different ways to select 2 subjects and 1 king from 6 people.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. A is 742. A is 397 less than B. B is 693 greater than C. Find the value of A-C. [/INST] Let's start by finding the value of B. We know that A is 397 less than B, so we can write the equation: B = A + 397 Since we know the value of A is 742, we can substitute that into the equation: B = 742 + 397 B = 1139 Now, we know that B is 693 greater than C, so we can write the equation: B = C + 693 We already found the value of B, which is 1139, so we can substitute that into the equation to find C: 1139 = C + 693 Now, let's solve for C: C = 1139 - 693 C = 446 Now that we have the values of A and C, we can find A - C: A - C = 742 - 446 A - C = 296 So, the value of A - C is 296.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Cheolsu's nine classmates are standing in a nonagonal shape facing each other. If every student plays rock-paper-scissors once with everyone except for the person next to him/her, how many times do all students play rock-paper-scissors? [/INST] There are 9 students, and each student will play rock-paper-scissors with every other student except for the two students standing next to them (since they are standing in a nonagonal shape). Each student has 9 - 1 = 8 other students in the class, but we need to subtract the 2 students standing next to them, so each student will play with 8 - 2 = 6 other students. Since there are 9 students, the total number of games played would be 9 * 6 = 54. However, this counts each game twice (once for each participant), so we need to divide by 2 to get the actual number of unique games played. Therefore, the total number of unique games played is 54 / 2 = 27. So, all students play rock-paper-scissors 27 times in total.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Dongkyun runs 8 laps around the playground 4 times a day, and Heejin runs 5/7 laps 10 times a day. Find who runs the playground more. [/INST] To find out who runs more, we need to calculate the total distance each person runs per day. For Dongkyun: He runs 8 laps around the playground 4 times a day. So, the total number of laps he runs per day is: 8 laps/run * 4 runs/day = 32 laps/day For Heejin: She runs 5/7 of a lap around the playground 10 times a day. So, the total number of laps she runs per day is: (5/7) laps/run * 10 runs/day = 50/7 laps/day Now, to compare the two, we need to have them in the same terms. Let's convert 50/7 laps/day to a decimal to make it easier to compare with Dongkyun's 32 laps/day. 50/7 laps/day ≈ 7.14 laps/day (rounded to two decimal places) Now we can compare: Dongkyun: 32 laps/day Heejin: 7.14 laps/day Clearly, Dongkyun runs more laps per day than Heejin.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. A cloud train with a length of 20 meters (m) is running at 288 centimeters (cm) per second. If this train took 25 seconds to completely pass the tunnel, find the length of the tunnel in meters (m). [/INST] First, we need to convert the speed of the cloud train from centimeters per second to meters per second. Since 1 meter is equal to 100 centimeters, we divide the speed in centimeters per second by 100 to get the speed in meters per second. Speed in meters per second = 288 cm/s ÷ 100 = 2.88 m/s Now, we know the train took 25 seconds to completely pass through the tunnel. To find the distance the train traveled in that time, we multiply the speed by the time: Distance traveled = Speed × Time Distance traveled = 2.88 m/s × 25 s = 72 meters This distance includes the length of the train itself plus the length of the tunnel. Since the train is 20 meters long, we subtract the length of the train from the total distance to find the length of the tunnel: Length of the tunnel = Distance traveled - Length of the train Length of the tunnel = 72 m - 20 m = 52 meters Therefore, the length of the tunnel is 52 meters.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Jaeho and Kyunghwan took a walk for the same amount of time. Jaeho walked a distance of 1/100 of 10.2 kilometers (km), and Kyunghwan walked a distance of 100 meters (m). Who walked more distances, Jaeho or Kyunghwan? [/INST] First, let's calculate the distance Jaeho walked. Jaeho walked 1/100 of 10.2 kilometers. \( \frac{1}{100} \times 10.2 \text{ km} = 0.102 \text{ km} \) Now, we need to convert 0.102 kilometers to meters to compare it with Kyunghwan's distance. There are 1000 meters in a kilometer, so: \( 0.102 \text{ km} \times 1000 \text{ m/km} = 102 \text{ m} \) Kyunghwan walked 100 meters. Comparing the two distances: - Jaeho walked 102 meters. - Kyunghwan walked 100 meters. Jaeho walked more distance than Kyunghwan.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Ji-hoon made a mistake while calculating and subtracted 7 from a number instead of multiplying by 7, and it became 0.45. Find out the answer Jihoon was originally looking for. [/INST] Let's denote the original number as \( x \). According to the mistake Ji-hoon made, he subtracted 7 from \( x \) instead of multiplying by 7, and the result was 0.45. So we can write the equation for the mistake as: \[ x - 7 = 0.45 \] To find the original number \( x \), we need to add 7 to both sides of the equation: \[ x = 0.45 + 7 \] \[ x = 7.45 \] Now that we have the original number, we can find the answer Ji-hoon was originally looking for by multiplying \( x \) by 7: \[ 7.45 \times 7 = 52.15 \] So the answer Ji-hoon was originally looking for is 52.15.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. 3 puppies and 7 chicks are playing in the yard of Junho's house. Find how many legs the puppies and chicks have together. [/INST] Puppies have 4 legs each, and chicks have 2 legs each. For the 3 puppies: 3 puppies * 4 legs/puppy = 12 legs For the 7 chicks: 7 chicks * 2 legs/chick = 14 legs Adding the legs of puppies and chicks together: 12 legs + 14 legs = 26 legs So, the puppies and chicks have a total of 26 legs together.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Find the certain number if the certain number multiplied by 7 minus 6 equals the certain number multiplied by 4 plus 12. [/INST] Let's denote the certain number as \( x \). According to the problem, we have the equation: \( 7x - 6 = 4x + 12 \) Now, let's solve for \( x \): First, we'll move all terms involving \( x \) to one side of the equation and constants to the other side: \( 7x - 4x = 12 + 6 \) Combine like terms: \( 3x = 18 \) Now, divide both sides by 3 to solve for \( x \): \( x = \frac{18}{3} \) \( x = 6 \) So, the certain number is 6.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. 3rd grade students from Min's school split into 18 15-seater buses to go on a field trip. If 3 seats are empty in each bus, how many 3rd grade students are there at Min's school? [/INST] If each 15-seater bus has 3 empty seats, then there are 15 - 3 = 12 students seated in each bus. Since there are 18 buses, the total number of 3rd grade students is 18 buses * 12 students/bus = 216 students.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. You want to create a three-digit number using 5, 9, and 2 once. When the difference between the two numbers made is the largest, find the difference. [/INST] To create the largest difference between two three-digit numbers using the digits 5, 9, and 2, we need to form the largest possible number and the smallest possible number with these digits. The largest number we can form with 5, 9, and 2 is 952 (using the digits in descending order). The smallest number we can form with 5, 9, and 2 is 259 (using the digits in ascending order). Now, we subtract the smaller number from the larger number to find the largest difference: 952 (largest number) - 259 (smallest number) = 693 So, the largest difference between the two numbers made with the digits 5, 9, and 2 is 693.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. 128 coins are scattered on the floor. If there are 12 more coins that are heads than coins that are tails, how many coins are heads? [/INST] Let's call the number of heads H and the number of tails T. We are given two pieces of information: 1. The total number of coins is 128, so H + T = 128. 2. There are 12 more heads than tails, so H = T + 12. We can substitute the second equation into the first to solve for T: H + T = 128 (T + 12) + T = 128 2T + 12 = 128 2T = 128 - 12 2T = 116 T = 116 / 2 T = 58 Now that we know there are 58 tails, we can find the number of heads by adding 12 to the number of tails: H = T + 12 H = 58 + 12 H = 70 So there are 70 coins with heads.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Roses were planted in one-third of the 2.4 square meters (m2) flower bed, and tulips were planted in the remaining one-quarter. Find the area of the area where the tulips are planted. [/INST] First, we need to find the area where the roses are planted. Since roses were planted in one-third of the 2.4 m² flower bed, we calculate this area as follows: Area for roses = (1/3) * 2.4 m² Area for roses = 0.8 m² Now, we need to find the remaining area of the flower bed that is not occupied by roses. This will be the total area minus the area for roses: Remaining area = Total area - Area for roses Remaining area = 2.4 m² - 0.8 m² Remaining area = 1.6 m² Since tulips were planted in one-quarter of the remaining area, we calculate the area for tulips as follows: Area for tulips = (1/4) * Remaining area Area for tulips = (1/4) * 1.6 m² Area for tulips = 0.4 m² Therefore, the area where the tulips are planted is 0.4 m².</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. The red confetti has a square shape with a side length of 11 centimeters (cm), and the blue confetti has a square shape with a side length of 5 centimeters (cm). What is the sum of the areas of the two pieces of colored paper in square centimeters (cm2)? [/INST] To find the sum of the areas of the two pieces of confetti, we need to calculate the area of each piece separately and then add them together. The area of a square is calculated by squaring the length of one of its sides. For the red confetti: Area = side length × side length Area = 11 cm × 11 cm Area = 121 cm² For the blue confetti: Area = side length × side length Area = 5 cm × 5 cm Area = 25 cm² Now, we add the areas of both pieces of confetti together to get the total area: Total area = Area of red confetti + Area of blue confetti Total area = 121 cm² + 25 cm² Total area = 146 cm² So, the sum of the areas of the two pieces of colored paper is 146 cm².</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Three more boys and 10 girls entered the class, and now the total number of girls became 22. If there were 5 more boys than girls initially, how many boys are still in the classroom? [/INST] Let's denote the initial number of girls as G and the initial number of boys as B. According to the information given, after 10 girls entered the class, the total number of girls became 22. So initially, there were: G + 10 = 22 From this, we can solve for G: G = 22 - 10 G = 12 Now, we know that initially, there were 5 more boys than girls. So: B = G + 5 B = 12 + 5 B = 17 This means there were initially 17 boys in the class. Now, three more boys entered the class. So the new number of boys in the class is: B + 3 = 17 + 3 B + 3 = 20 Therefore, there are now 20 boys in the classroom.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. In Jungkook's class, there are 9 students who wear glasses and 16 students who do not wear glasses. How many students are there? [/INST] To find the total number of students in Jungkook's class, we simply add the number of students who wear glasses to the number of students who do not wear glasses. Number of students who wear glasses = 9 Number of students who do not wear glasses = 16 Total number of students = 9 (who wear glasses) + 16 (who do not wear glasses) Total number of students = 25 So, there are 25 students in Jungkook's class.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. When you add 2 to a number and then subtract 3, you get 7. Find out this number [/INST] Let's call the number you're trying to find "x". According to the problem, when you add 2 to x and then subtract 3, you get 7. We can write this as an equation: x + 2 - 3 = 7 Now, let's solve for x: x + 2 - 3 = 7 x - 1 = 7 (combining the +2 and -3 into -1) Now, add 1 to both sides to isolate x: x - 1 + 1 = 7 + 1 x = 8 So the number you're looking for is 8.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. There is a prism with a sum of the number of vertices, faces, and corners is 50. How many edges of the pyramid have the same base shape as the prism? [/INST] To solve this problem, we need to use Euler's formula for polyhedra, which states that for any convex polyhedron: V - E + F = 2 where V is the number of vertices, E is the number of edges, and F is the number of faces. From the given information, we have: V + F + C = 50 However, the term "corners" is a bit ambiguous, as corners typically refer to vertices in the context of polyhedra. Assuming that "corners" is a mistaken term and should be "edges" (E), we can rewrite the equation as: V + E + F = 50 Now, let's use Euler's formula to find the relationship between V, E, and F for the prism: V - E + F = 2 We can rearrange this equation to solve for E: E = V + F - 2 Since we know that V + E + F = 50, we can substitute E in the above equation: E = (50 - E) - 2 Now, let's solve for E: E = 50 - E - 2 2E = 48 E = 24 So, the prism has 24 edges. Now, let's find the number of edges of the pyramid that has the same base shape as the prism. A pyramid has one less edge on the base than the prism because the base of the pyramid is the same as one of the faces of the prism, and the rest of the edges of the pyramid come from the vertices of the base to the apex. Let's denote the number of edges on the base of the prism as B. Since a prism has two congruent bases, the total number of edges on the bases of the prism is 2B. The remaining edges of the prism are the ones that connect the corresponding vertices of the two bases, which is equal to the number of vertices on one base (also B). So, for the prism, we have: E (total edges of prism) = 2B (edges on bases) + B (vertical edges) 24 = 2B + B 24 = 3B B = 24 / 3 B = 8 The base of the prism has 8 edges, which means the base is an octagon. Now, for the pyramid with an octagonal base, the number of edges will be the number of edges on the base (8) plus the number of edges from the vertices of the base to the apex (also 8, since there is one edge from each vertex of the base to the apex). Therefore, the pyramid has 8 (base edges) + 8 (edges to apex) = 16 edges.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. If you add up Yoongi and Hoseok's ages this year, it is 16. Hoseok is 2 years younger than Yoongi. How old is Yoongi this year? [/INST] Let's denote Yoongi's age as Y and Hoseok's age as H. According to the information given: 1) Y + H = 16 (The sum of their ages is 16) 2) Y = H + 2 (Hoseok is 2 years younger than Yoongi) Now we can substitute the second equation into the first one: (H + 2) + H = 16 Combine like terms: 2H + 2 = 16 Subtract 2 from both sides: 2H = 14 Divide both sides by 2: H = 7 Now that we know Hoseok's age, we can find Yoongi's age by using the second equation: Y = H + 2 Y = 7 + 2 Y = 9 Yoongi is 9 years old this year.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. If there are 6 students A, B, C, D, E, and F, find the number of ways to select 2 representatives and 1 secretary. [/INST] To select 2 representatives and 1 secretary from 6 students, we can approach the problem in two steps: Step 1: Select 2 representatives from the 6 students. Step 2: Select 1 secretary from the remaining 4 students (since 2 have already been chosen as representatives). Step 1: The number of ways to choose 2 representatives from 6 students is given by the combination formula \( C(n, k) = \frac{n!}{k!(n-k)!} \), where \( n \) is the total number of items, \( k \) is the number of items to choose, and \( ! \) denotes factorial. For our case, \( n = 6 \) and \( k = 2 \), so the number of ways to choose 2 representatives is: \[ C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6!}{2!4!} = \frac{6 \times 5}{2 \times 1} = 15 \] Step 2: Now, we have 4 students left. The number of ways to choose 1 secretary from these 4 students is simply 4, since there are 4 options and we are choosing 1. Finally, to find the total number of ways to select 2 representatives and 1 secretary, we multiply the results of Step 1 and Step 2: Total ways = Ways to choose representatives × Ways to choose secretary Total ways = 15 × 4 Total ways = 60 Therefore, there are 60 different ways to select 2 representatives and 1 secretary from 6 students.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Subtracting 2.95 twice from a number gives 9.28. Find this number. [/INST] Let's call the number we're looking for "x". According to the problem, if we subtract 2.95 from x twice, we get 9.28. We can set up the equation like this: x - 2.95 - 2.95 = 9.28 Now, we combine the like terms (the two instances of subtracting 2.95): x - (2.95 + 2.95) = 9.28 x - 5.90 = 9.28 Now, to find x, we add 5.90 to both sides of the equation: x = 9.28 + 5.90 x = 15.18 So the number we're looking for is 15.18.</s>
<s>[INST] You are a math instructor and you solve math word problems. Please solve the following math problem. Find the total volume if you stack 7 rows, 5 columns, and 3 layers of Legos, each measuring 1 centimeter (cm) in length, width, and height. [/INST] To find the total volume of the stacked Legos, we need to calculate the volume of a single Lego and then multiply it by the total number of Legos. The volume of a single Lego (assuming it's a perfect cube) is: Length x Width x Height = 1 cm x 1 cm x 1 cm = 1 cubic centimeter (cm³) The total number of Legos is the product of the number of rows, columns, and layers: 7 rows x 5 columns x 3 layers = 105 Legos Now, we multiply the volume of a single Lego by the total number of Legos to find the total volume: 1 cm³ x 105 = 105 cm³ So, the total volume of the stacked Legos is 105 cubic centimeters.</s>