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"I need to find the number of entrances by dividing the total number of people waiting by the number of people at each entrance.\n\nLet's denote the number of entrances as \\( n \\).\n\nThe total number of people waiting is 1415, and the number of people at each entrance is 283.\n\nI can set up the equation: $$283 ... | [
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] | When they got there, they saw that SFL is already filled with people. Every entrance has a long line, with 283 people waiting to get in. If there are 1415 people in total waiting to get in, how many entrances does SFL have? | 5 |
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"I need to find the total number of students in Buddy's gym class.\n\nSince the first group represents 20% of the students, the second group represents 30%, and the third group represents 50%, I can set up the following equation to represent the total number of students:\n\n$$0.2x + 0.3x + 0.5x = 37$$\n\nwhere $$x$... | [
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] | After recess, Buddy changed clothes for gym class. Down at the gym, all the students were divided into three groups. The first group represents 20% of the students, the second group represents 30%, and the third group, consisting of 37 students, represents the remaining 50%. How many students are in Buddy's gym class i... | 74 |
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"I need to find the total square footage of glass needed to cover all five walls.\n\nTwo walls will be completely covered with rectangular glass, so I need to find the area of two rectangles.\n\nThe dimensions of the rectangular glass are 30 feet by 12 feet, so the area of one rectangle is $$30 \\times 12 = 360$$ s... | [
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] | James is building a hall of mirrors with five walls. Two of those walls will be completely covered with rectangular glass, one with a large triangular glass piece, and the remaining two walls will be covered with trapezoidal glass pieces. The dimensions of the rectangular glass are 30 feet by 12 feet, the triangular gl... | 1308 |
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"I need to find the total number of people both boats can transport in these 2 days.\n\nOn the first day, Boat A makes 7 trips, and each trip can take up to 20 people.\n\nSo, the total number of people Boat A can transport on the first day is $$7 \\times 20 = 140$$.\n\nOn the same day, Boat B makes 5 trips, and eac... | [
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] | During one day, there are 7 boat trips by Boat A and 5 boat trips by Boat B through the lake. Boat A can take up to 20 people during one trip, while Boat B can take up to 15 people during one trip. On the second day, Boat A can only make 5 trips, while Boat B can make 6 trips. How many people can both the boats transpo... | 405 |
[
"I need to find the probability of the coin landing tails up exactly twice in 3 consecutive flips.\n\nSince the coin has an equal probability of landing heads up or tails up each time it is flipped, I can assume that the probability of the coin landing tails up is $$\\frac{1}{2}$$.\n\nTo find the probability of the... | [
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] | if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exectly twice in 3 consecutive flips ? | 0.375 |
[
"I know that Peter drew 8 pictures, and Quincy drew 20 more than Peter.\n\nSo, Quincy drew $$8 + 20 = 28$$ pictures.\n\nI also know that Sam drew 15 more than Randy.\n\nLet's call the number of pictures Randy drew \\( r \\).\n\nThen, Sam drew \\( r + 15 \\) pictures.\n\nThe total number of pictures drawn is 75, so ... | [
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] | Randy, Peter, Quincy, and Sam all drew pictures. Peter drew 8 pictures. Quincy drew 20 more pictures than Peter, and Sam drew 15 more pictures than Randy. If they drew a total of 75 pictures altogether, how many pictures did Randy draw? | 12 |
[
"I need to find the time taken by pipe A to fill the tank alone.\n\nLet's denote the time taken by pipe A to fill the tank alone as \\( t \\) hours.\n\nThe rate at which pipe A fills the tank is $$\\frac{1}{t}$$ tanks per hour.\n\nSince pipe B can fill the tank in 45 hours, its rate is $$\\frac{1}{45}$$ tanks per h... | [
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] | Two pipes A and B can fill a tank in some hours and 45 hours respectively. If both the pipes are opened simultaneously, it takes 18 hours to fill the tank. How much time will pipe A take to fill the tank alone? | 30 |
[
"I need to find the length of the altitude of the isosceles triangle in terms of 'a'.\n\nSince circle X has a circumference of 14π, I can find its radius by using the formula for the circumference of a circle: $$C = 2\\pi r$$.\n\nGiven that $$C = 14\\pi$$, I can solve for the radius of circle X:\n$$14\\pi = 2\\pi r... | [
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"However, this is not possible, as the altitude cannot be zero",
"Since \\( a = \\frac{7}{2} \\), I can simplify the equation: $$h = \\frac{2\\pi 7^",
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] | Two circles, X and Y, with the same area are inscribed in a rectangle. An isosceles triangle with base on one side of the rectangle has its vertex touching the circumference of circle Y. Circle X has a circumference of 14π. If half of the radius of circle Y is 'a', find the length of the altitude of the isosceles trian... | a\sqrt{3} |
[
"I need to find the score for mathematics based on the given average score and the scores in other subjects.\n\nLet's denote the score for mathematics as \\( m \\).\n\nThe average score is given as 88, which is the sum of all scores divided by the total number of subjects.\n\nSince there are four subjects (ethics, ... | [
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] | Hyejin's monthly evaluation score is 82 for ethics, 90 for Korean language, 88 for science, and 84 for social studies. The score for mathematics is unknown. When the average score is 88, what is the score for mathematics? | 96 |
[
"I need to find Ram's monthly salary, given the relationships between Abhinav's, Shyam's, and Ram's salaries.\n\nFirst, I know that Abhinav's annual salary is Rs. 1.92 lakhs.\n\nSince there are 12 months in a year, I can find Abhinav's monthly salary by dividing his annual salary by 12:\n$$\\frac{1.92 \\text{ lakhs... | [
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] | 10 percent of Ram's monthly salary is equal to 8 percent of Shyam's monthly salary. Shyam's monthly salary is twice Abhinav's monthly salary. Abhinav's annual salary is Rs. 1.92 lakhs. What is Ram's monthly salary? | 25,600 |
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