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0.05 | A farmer has a total of 60 animals, consisting of cows and chickens. If the number of cows is twice the number of chickens, how many cows and how many chickens does the farmer have? | Let's denote the number of chickens as C and the number of cows as W. According to the problem, we know two things: 1) The total number of animals is 60, so C + W = 60. 2) The number of cows is twice the number of chickens, which gives us W = 2C. Now we can substitute W in the first equation with 2C: C + 2C = 60. This ... |
0.05 | In a class of 30 students, 18 are taking mathematics, 15 are taking science, and 10 are taking both subjects. How many students are taking only one subject? Show your work. | Let M be the set of students taking mathematics and S be the set of students taking science. We know that |M| = 18, |S| = 15, and |M ∩ S| = 10 (students taking both). To find the number of students taking only mathematics, we calculate |M| - |M ∩ S| = 18 - 10 = 8. For those taking only science, we do |S| - |M ∩ S| = 15... |
0.05 | A box contains red, blue, and green marbles. There are three times as many red marbles as blue marbles, and four more green marbles than red marbles. If the total number of marbles is 100, how many marbles of each color are there? | Let B represent the number of blue marbles. Then the number of red marbles R would be 3B, and the number of green marbles G would be R + 4 = 3B + 4. The total number of marbles is given by B + R + G = 100. Substituting for R and G gives us B + 3B + (3B + 4) = 100. Simplifying this leads to 7B + 4 = 100. Subtracting 4 f... |
0.05 | A certain school has a student-to-teacher ratio of 12:1. If there are 24 teachers at the school, how many students are enrolled? Provide your reasoning. | The student-to-teacher ratio indicates that for every teacher, there are 12 students. Given that there are 24 teachers, we can find the total number of students by multiplying the number of teachers by the ratio of students per teacher. Thus, Total Students = Number of Teachers * Ratio = 24 * 12 = 288. Therefore, the s... |
0.05 | If five cats can catch five mice in five minutes, how many cats are needed to catch 100 mice in 50 minutes? Explain your logic step-by-step. | From the information provided, we understand that 5 cats catch 5 mice in 5 minutes. This means that 1 cat catches 1 mouse in 5 minutes. To determine how many mice one cat can catch in 50 minutes, we divide 50 minutes by 5 minutes/mouse, resulting in 10 mice per cat in 50 minutes. Next, if we need to catch 100 mice, we ... |
0.05 | In a family, there are parents and children. Each parent has 3 children. If there are 6 parents in the family, how many children are there in total? Provide your steps. | We start by identifying the relationship between parents and children. Each parent has 3 children. Since there are 6 parents, we can calculate the total number of children by multiplying the number of parents by the number of children each parent has: Total Children = Number of Parents * Children per Parent = 6 * 3 = 1... |
0.05 | A bookstore sells novels and textbooks. If the store sold 120 novels and twice as many textbooks as novels, what was the total number of books sold? Show your calculations. | First, we identify the number of novels sold, which is given as 120. The problem states that the number of textbooks sold is twice the number of novels. Therefore, Textbooks Sold = 2 * Novels Sold = 2 * 120 = 240. To find the total number of books sold, we add the number of novels and textbooks together: Total Books So... |
0.05 | In a competition, there are three rounds. A contestant earns 5 points for each correct answer and loses 2 points for each incorrect answer. If a contestant answered 15 questions correctly and 5 incorrectly, what is their final score? Explain your process. | To calculate the final score, we first determine the points earned from correct answers. Points from Correct Answers = Correct Answers * Points per Correct Answer = 15 * 5 = 75 points. Next, we calculate the points lost due to incorrect answers: Points Lost from Incorrect Answers = Incorrect Answers * Points Lost per I... |
0.05 | A library has a collection of fiction and non-fiction books. If the number of fiction books is 150 more than twice the number of non-fiction books, and the total number of books in the library is 600, how many fiction and non-fiction books are there? Provide your reasoning. | Let N represent the number of non-fiction books. According to the problem, the number of fiction books F can be expressed as F = 2N + 150. The total number of books gives us the equation N + F = 600. Substituting F into this equation yields N + (2N + 150) = 600. Combining like terms results in 3N + 150 = 600. By subtra... |
0.05 | A farmer has chickens and cows. If the total number of legs on his farm is 28, and he has twice as many chickens as cows, how many chickens and cows does he have? Show your work. | Let's denote the number of cows as C and the number of chickens as H. According to the problem, we know two things:
1. The total number of legs is 28.
2. There are twice as many chickens as cows, so H = 2C.
Now, let's calculate the total number of legs:
- Each cow has 4 legs, so the total legs from cows is 4C.
- Each ... |
0.05 | In a family, each parent has three children. If there are four parents in total, how many children do they have altogether? Provide your reasoning step-by-step. | To solve this, we start by determining how many children each parent has. Each parent has 3 children. Since there are 4 parents, we can multiply the number of parents by the number of children per parent:
Total children = Number of parents * Children per parent
= 4 * 3
= 12.
Thus, altogether, the family has 12 children... |
0.05 | A bookstore sells books at different prices. If the average price of a book is $15 and the store sold 40 books last month, what was the total revenue generated from book sales? Explain your calculations. | To find the total revenue generated from book sales, we use the formula:
Total Revenue = Average Price per Book * Number of Books Sold.
Here, the average price of a book is $15, and the number of books sold is 40. So we calculate:
Total Revenue = 15 * 40 = 600.
Therefore, the total revenue generated from book sales las... |
0.05 | There are five friends: Alice, Bob, Charlie, David, and Eve. If Alice knows Bob and Charlie, Bob knows Charlie and David, Charlie knows David and Eve, and David knows Eve and Alice, who knows whom? Analyze the connections step-by-step. | We will analyze the relationships based on the information given:
1. Alice knows Bob and Charlie.
2. Bob knows Charlie and David.
3. Charlie knows David and Eve.
4. David knows Eve and Alice.
From this, we can summarize the knowledge network:
- Alice knows: Bob, Charlie.
- Bob knows: Alice, Charlie, David.
- Charlie k... |
0.05 | If a company has 200 employees and 60% of them are women, how many men are employed by the company? Provide detailed steps to arrive at the answer. | First, we need to determine how many women are employed by the company. We know that 60% of the employees are women:
Number of women = Total Employees * Percentage of Women
= 200 * 0.60
= 120 women.
Next, to find out how many men are employed, we subtract the number of women from the total number of employees:
Number ... |
0.05 | In a class of students, 30% passed mathematics, 25% passed science, and 10% passed both subjects. If there are 100 students in total, how many students failed both subjects? Show your calculations clearly. | To find out how many students failed both subjects, we first calculate those who passed either subject using the principle of inclusion-exclusion:
Let A be the set of students who passed mathematics, and B be the set of students who passed science.
The number of students who passed at least one subject is:
|A ∪ B| = |A... |
0.05 | If a triangle has angles measuring 35 degrees and 75 degrees, what is the measure of the third angle? Explain your reasoning. | In any triangle, the sum of all interior angles equals 180 degrees. Given two angles, we can find the third angle by subtracting the sum of the known angles from 180 degrees:
Let Angle 1 = 35 degrees and Angle 2 = 75 degrees.
Sum of known angles = 35 + 75 = 110 degrees.
Now, we find the third angle:
Third Angle = 180 ... |
0.05 | A group of friends decided to share their expenses equally. If they spent a total of $240 on dinner and there were 8 friends, how much did each person pay? Show your calculation process. | To find out how much each person paid, we divide the total expense by the number of friends:
Total Expense = $240,
Number of Friends = 8.
Each person's share = Total Expense / Number of Friends
= 240 / 8
= 30.
Therefore, each friend paid $30. |
0.05 | A train leaves a station and travels north at a constant speed. If it takes 3 hours to reach its destination and covers a distance of 150 miles, what is the average speed of the train? Provide your solution step-by-step. | To find the average speed of the train, we use the formula:
Average Speed = Total Distance / Total Time.
Here, the total distance covered is 150 miles, and the time taken is 3 hours.
Calculating the average speed:
Average Speed = 150 miles / 3 hours = 50 miles per hour.
Thus, the average speed of the train is 50 miles... |
0.05 | A farmer has a total of 100 animals, consisting of cows and chickens. If there are twice as many chickens as cows, how many cows does the farmer have? Show your work. | Let's denote the number of cows as C and the number of chickens as H. According to the problem, we know two things:
1. The total number of animals is 100, so C + H = 100.
2. There are twice as many chickens as cows, which gives us H = 2C.
Now we can substitute the second equation into the first:
C + 2C = 100,
3C = 10... |
0.05 | In a class of 30 students, each student plays either soccer or basketball. If 18 students play soccer and 12 students play basketball, how many students play both sports? Provide step-by-step reasoning. | Let S represent the number of students who play soccer, B represent those who play basketball, and X represent those who play both sports. We know:
1. Total students = 30
2. Students playing soccer = S = 18
3. Students playing basketball = B = 12
Using the principle of inclusion-exclusion for sets, we can express the ... |
0.05 | A clock shows the time as 3:15. What is the angle between the hour hand and the minute hand at this time? Explain your calculations. | To calculate the angle between the hour and minute hands on a clock, we use the following method:
1. Each hour represents 30 degrees (360 degrees/12 hours).
2. At 3:00, the hour hand is at 90 degrees (3 hours * 30 degrees/hour).
3. By 3:15, the hour hand moves further. Since it moves 0.5 degrees per minute (30 degrees/... |
0.05 | If five times a certain number decreased by 9 equals 16, what is the number? Show your steps clearly. | Let the unknown number be represented as N. From the problem statement, we set up the equation:
5N - 9 = 16.
To solve for N, we first add 9 to both sides:
5N = 16 + 9,
5N = 25.
Next, we divide both sides by 5 to isolate N:
N = 25 / 5,
N = 5.
Therefore, the number is 5. |
0.05 | A box contains red, blue, and green marbles. If there are 40 marbles in total, with three times as many red marbles as blue marbles and four more green marbles than blue marbles, how many blue marbles are there? Provide detailed reasoning. | Let B represent the number of blue marbles. Then according to the problem:
1. Red marbles = 3B (three times as many red as blue)
2. Green marbles = B + 4 (four more green than blue)
The total number of marbles can be expressed as:
B + 3B + (B + 4) = 40.
Combining like terms results in:
5B + 4 = 40.
Subtracting 4 from... |
0.05 | A rectangle's length is twice its width. If the perimeter of the rectangle is 48 units, what are the dimensions of the rectangle? Include your calculations. | Let W represent the width of the rectangle. Given that the length L is twice the width, we can write:
L = 2W.
The formula for the perimeter P of a rectangle is given by:
P = 2(L + W).
Substituting the known perimeter value:
48 = 2(2W + W).
Simplifying this expression:
48 = 2(3W),
48 = 6W.
Now, dividing both sides by ... |
0.05 | There are 120 students in a school choir. If 75% of them are girls, how many boys are in the choir? Provide a clear breakdown of your reasoning. | First, let's calculate the number of girls in the choir. Since 75% of the 120 students are girls, we compute:
Number of girls = 75% of 120 = 0.75 * 120 = 90.
Next, to find the number of boys, we subtract the number of girls from the total number of students:
Number of boys = Total students - Number of girls = 120 - 90... |
0.05 | A bookstore sells books at $15 each. If a customer buys 10 books and pays with a $200 bill, how much change will they receive? Show your calculation process. | To find out how much change the customer receives, we first need to calculate the total cost of the books purchased. The price per book is $15, and the customer buys 10 books:
Total cost = Price per book * Number of books = 15 * 10 = $150.
Next, we subtract the total cost from the amount paid:
Change = Amount paid - T... |
0.05 | A farmer has a total of 120 apples and oranges. If he has three times as many apples as oranges, how many apples does he have? Show your work. | Let's denote the number of oranges as 'x'. Since the farmer has three times as many apples as oranges, we can express the number of apples as '3x'. Now, according to the problem, the total number of fruits is 120. Therefore, we can set up the equation: x (oranges) + 3x (apples) = 120. This simplifies to 4x = 120. To fi... |
0.05 | In a class of 30 students, 18 students play soccer, 12 students play basketball, and 6 students play both sports. How many students do not play either sport? Provide detailed reasoning. | To solve this, we will use the principle of inclusion-exclusion. Let A be the set of students who play soccer and B be the set of students who play basketball. We know that |A| = 18, |B| = 12, and |A ∩ B| = 6 (students who play both). According to the formula for union of two sets: |A ∪ B| = |A| + |B| - |A ∩ B|. Pluggi... |
0.05 | If a rectangle's length is twice its width and the perimeter is 48 units, what are the dimensions of the rectangle? Explain your steps clearly. | Let the width of the rectangle be 'w' units. Then the length would be '2w' units since it is twice the width. The formula for the perimeter P of a rectangle is given by P = 2(length + width). Substituting our expressions into the formula gives us: 48 = 2(2w + w). Simplifying this results in: 48 = 2(3w), which further s... |
0.05 | A store sells pencils for $0.50 each and erasers for $1.00 each. If a customer buys a total of 20 items and spends $15, how many pencils did they buy? Include your reasoning. | Let 'p' represent the number of pencils and 'e' represent the number of erasers. We have two equations based on the information provided: p + e = 20 (total items) and 0.5p + 1.0e = 15 (total cost). From the first equation, we can express e in terms of p: e = 20 - p. Substituting this expression into the second equation... |
0.05 | A family has a pet dog and a pet cat. The dog weighs twice as much as the cat. If the combined weight of the dog and cat is 36 pounds, what is the weight of the dog? Show your calculations step-by-step. | Let the weight of the cat be 'c' pounds. Consequently, the dog's weight would be '2c' pounds because it weighs twice as much as the cat. The total weight of both pets can be expressed as: c + 2c = 36. This simplifies to 3c = 36. To isolate 'c', we divide both sides by 3: c = 12. Therefore, the cat weighs 12 pounds. To ... |
0.05 | There are five friends: Alice, Bob, Charlie, David, and Eva. Each friend has a different favorite color among red, blue, green, yellow, and purple. If Alice’s favorite color is not red or blue, Bob likes blue, Charlie doesn’t like yellow, David likes red, and Eva doesn't like purple, what is each friend's favorite colo... | From the clues given, we can deduce the following: Bob likes blue; David likes red. Since Alice cannot like red or blue, her options are green, yellow, or purple. Charlie does not like yellow, leaving him with green or purple. Since David likes red and Bob likes blue, Eva must choose between yellow or green, but she ca... |
0.05 | A train departs from Station A to Station B every hour starting at 9 AM. It takes 2 hours to reach Station B. At the same time, another train departs from Station B to Station A every hour starting at 10 AM. If the second train also takes 2 hours to reach Station A, how many trains are on the route between the two stat... | At 11 AM, let's analyze the situation. The first train left Station A at 10 AM and is currently en route to Station B, arriving at 12 PM. The first train that departed at 9 AM is still traveling and will arrive at 11 AM. So far, we have two trains from Station A to Station B. Now considering the trains from Station B: ... |
0.05 | A box contains 3 red balls, 5 blue balls, and 2 green balls. If you randomly select 2 balls without replacement, what is the probability that both balls are blue? Show your calculation process. | First, we need to determine the total number of balls in the box: 3 red + 5 blue + 2 green = 10 balls. The probability of selecting 2 blue balls can be calculated using combinations. The number of ways to choose 2 blue balls from 5 is denoted as C(5, 2). The total number of ways to choose any 2 balls from 10 is C(10, 2... |
0.05 | A company produces gadgets. In January, they produced 500 gadgets. Every month thereafter, production increases by 10% compared to the previous month. How many gadgets will they produce in March? Provide a clear breakdown of your calculations. | The initial production in January is 500 gadgets. For February, we apply a 10% increase: Production in February = 500 + (10% of 500) = 500 + 50 = 550 gadgets. For March, we again apply a 10% increase to February's production: Production in March = 550 + (10% of 550) = 550 + 55 = 605 gadgets. Therefore, the company will... |
0.05 | A farmer has a total of 60 apples and oranges. If he has twice as many apples as oranges, how many apples and how many oranges does he have? Show your work. | Let's denote the number of oranges as O and the number of apples as A. According to the problem, we know two things:
1. The total number of fruits is 60: A + O = 60.
2. The number of apples is twice the number of oranges: A = 2O.
Now, we can substitute the second equation into the first one:
2O + O = 60.
This simplifi... |
0.05 | In a certain class, there are three times as many girls as boys. If the total number of students in the class is 48, how many boys and how many girls are there? Explain your reasoning step-by-step. | Let B represent the number of boys and G represent the number of girls. We know from the problem:
1. The total number of students is 48: B + G = 48.
2. There are three times as many girls as boys: G = 3B.
We can substitute the second equation into the first:
B + 3B = 48.
This simplifies to:
4B = 48.
Dividing both side... |
0.05 | A book costs $15 more than a magazine. If the total cost of both items is $45, what is the price of each item? Provide detailed steps. | Let M be the price of the magazine and B be the price of the book. From the problem, we have:
1. B = M + 15 (the book costs $15 more than the magazine).
2. B + M = 45 (the total cost of both items is $45).
Substituting the first equation into the second:
(M + 15) + M = 45.
This simplifies to:
2M + 15 = 45.
Subtracting... |
0.05 | If you roll two six-sided dice, what is the probability that the sum of the numbers rolled will be greater than 8? Show your calculations clearly. | To find the probability, we need to determine two things: the total number of possible outcomes when rolling two dice and the number of favorable outcomes where the sum is greater than 8.
The total number of outcomes when rolling two dice is:
6 (sides on die 1) * 6 (sides on die 2) = 36.
Next, let's identify the comb... |
0.05 | You have a basket containing red, blue, and green marbles. If there are 12 red marbles, 8 blue marbles, and 4 green marbles, what fraction of the marbles are blue? Provide the solution with steps. | First, we need to find the total number of marbles in the basket. We add the number of each color together:
Total marbles = Red + Blue + Green = 12 + 8 + 4 = 24.
Next, we want to find the fraction of the marbles that are blue. Since there are 8 blue marbles, the fraction is:
Fraction of blue marbles = Number of blue m... |
0.05 | A train leaves station A heading towards station B at 3 PM. It travels at a speed of 60 km/h. Another train leaves station B towards station A at 4 PM traveling at 90 km/h. At what time will they meet if the distance between the stations is 300 km? Show your working process. | Let's denote the time it takes for the trains to meet after the first train departs as T hours. The first train starts at 3 PM and travels for T hours, while the second train starts an hour later at 4 PM and travels for (T - 1) hours.
The distance covered by the first train is:
Distance = Speed × Time = 60T.
The dist... |
0.05 | A family consists of parents and children. If there are 4 parents and each parent has 3 children, how many individuals are in the family? Explain your thought process. | To solve this, we start by identifying the components of the family:
1. There are 4 parents.
2. Each parent has 3 children.
To find the total number of children, we multiply the number of parents by the number of children per parent:
Total children = Number of parents × Children per parent = 4 × 3 = 12.
Now, we can f... |
0.05 | If a rectangle's length is twice its width and the perimeter is 48 cm, what are the dimensions of the rectangle? Provide detailed steps. | Let W represent the width of the rectangle. Then the length L can be expressed as:
L = 2W.
The formula for the perimeter P of a rectangle is given by:
P = 2(L + W).
According to the problem, the perimeter is 48 cm, so we set up the equation:
2(L + W) = 48.
Substituting L with 2W gives:
2(2W + W) = 48.
This simplifie... |
0.05 | A farmer has a certain number of sheep and cows. If he has 12 more sheep than cows, and the total number of animals is 48, how many cows does he have? Show your work. | Let's denote the number of cows as C and the number of sheep as S. According to the problem, we have two pieces of information:
1. S = C + 12 (the farmer has 12 more sheep than cows)
2. S + C = 48 (the total number of animals is 48)
Now, we can substitute the first equation into the second:
(C + 12) + C = 48
This sim... |
0.05 | In a class of students, if each student shakes hands with every other student exactly once, and there are 15 students in total, how many handshakes occur? Explain your reasoning step-by-step. | To find out how many unique handshakes occur among 15 students, we can use the formula for combinations since each handshake involves choosing 2 students from the group. The formula for combinations is given by:
C(n, k) = n! / [k!(n-k)!]
where n is the total number of students and k is the number of students involved... |
0.05 | A man has three times as much money as his friend. Together they have $240. How much money does each person have? Provide detailed steps. | Let’s denote the amount of money the friend has as F. Then, according to the problem, the man has 3F (three times what the friend has). Together, their total amounts add up to $240:
F + 3F = 240
4F = 240
Now, divide both sides by 4:
F = 60
So, the friend has $60. Now we can find out how much the man has:
Man's amoun... |
0.05 | If a rectangle has a length that is twice its width and the perimeter is 72 units, what are the dimensions of the rectangle? Show your calculations. | Let’s denote the width of the rectangle as W. Since the length is twice the width, we can express it as L = 2W. The formula for the perimeter P of a rectangle is given by:
P = 2L + 2W
Substituting the known values:
72 = 2(2W) + 2W
72 = 4W + 2W
72 = 6W
Now, divide both sides by 6:
W = 12
Now we can find the length:
L... |
0.05 | A box contains red, blue, and green marbles. If the ratio of red to blue marbles is 3:5 and the ratio of blue to green marbles is 4:7, how many green marbles are there if there are 60 blue marbles? Include your reasoning. | Given that there are 60 blue marbles, we can determine the number of red and green marbles using the ratios provided.
First, let's analyze the ratio of red to blue marbles, which is 3:5. This means for every 5 blue marbles, there are 3 red marbles. Therefore, if there are 60 blue marbles, we can set up a proportion:
... |
0.05 | A train leaves a station traveling north at a speed of 80 km/h. Another train leaves the same station 30 minutes later traveling south at a speed of 100 km/h. How far apart are the trains after 2 hours from when the first train left? Explain your thought process. | First, let’s calculate how far the first train travels in 2 hours. Since it leaves first and travels for 2 hours at 80 km/h:
Distance of Train 1 = Speed * Time = 80 km/h * 2 h = 160 km.
Now, the second train leaves 30 minutes later, which is 0.5 hours. By the time the first train has traveled for 2 hours, the second t... |
0.05 | There are four friends: Alice, Bob, Charlie, and Dana. Alice is older than Bob but younger than Charlie. Bob is younger than Dana. Who is the youngest among them? Provide a logical deduction. | Let’s analyze the age relationships step-by-step:
1. We know Alice is older than Bob, so A > B.
2. Alice is also younger than Charlie, meaning C > A.
3. Additionally, Bob is younger than Dana, indicating D > B.
From these statements, we can deduce the following order based on age:
Charlie > Alice > Bob < Dana.
Since ... |
0.05 | A store sells apples at $2 each and oranges at $3 each. If a customer buys a total of 10 fruits for $24, how many apples did the customer buy? Show your work. | Let’s denote the number of apples bought as A and the number of oranges as O. We have two equations based on the information provided:
1. A + O = 10 (total number of fruits)
2. 2A + 3O = 24 (total cost of fruits)
From the first equation, we can express O in terms of A:
O = 10 - A.
Now, substituting this expression fo... |
0.05 | In a family, the mother is twice as old as her son. Five years ago, the sum of their ages was 50. What are their current ages? Provide a step-by-step solution. | Let’s denote the son's current age as S and the mother's current age as M. From the problem, we have:
1. M = 2S (the mother is twice as old as her son).
2. Five years ago, the sum of their ages was 50:
(M - 5) + (S - 5) = 50.
Substituting the first equation into the second:
(2S - 5) + (S - 5) = 50.
This simplifies to:... |
0.05 | A farmer has a certain number of apples. He gives 1/4 of his apples to his neighbor and then finds that he has 60 apples left. How many apples did the farmer originally have? Show your work. | Let's denote the original number of apples as x. According to the problem, after giving away 1/4 of his apples, the farmer is left with 60 apples. This can be expressed mathematically as follows:
1. The amount given away is (1/4)x.
2. Therefore, the remaining apples can be represented as:
Remaining apples = Origin... |
0.05 | In a class of students, 70% passed mathematics, 60% passed science, and 50% passed both subjects. What percentage of students passed at least one subject? Provide your reasoning. | To determine the percentage of students who passed at least one subject, we can use the principle of inclusion-exclusion. Let A represent the set of students who passed mathematics and B represent those who passed science.
1. We know from the problem:
P(A) = 70%
P(B) = 60%
P(A ∩ B) = 50% (those who passed bot... |
0.05 | A company produces three types of products: A, B, and C. Product A accounts for 30% of sales, product B accounts for 50%, and product C accounts for the rest. If the total sales are $200,000, how much money does each product generate in sales? Explain your steps. | Let’s break down the sales for each product based on their percentages:
1. Total sales = $200,000.
2. For product A, which accounts for 30% of sales:
Sales from A = 30% of $200,000 = 0.30 * 200,000 = $60,000.
3. For product B, which accounts for 50% of sales:
Sales from B = 50% of $200,000 = 0.50 * 200,000 = $10... |
0.05 | A book club has 12 members. Each member reads an average of 8 books per year. However, 3 members read twice as many books as the others. How many books do all members read together in a year? Show your calculations. | First, let's calculate the total number of books read by the regular members and the additional readers separately:
1. There are 12 members in total, and 3 of them read twice as many books as the other 9 members.
2. The 9 regular members read 8 books each:
Books read by regular members = 9 * 8 = 72 books.
3. The 3 ... |
0.05 | A school has 240 students enrolled. If 25% of the students play soccer, 15% play basketball, and 10% play both sports, what percentage of students play at least one sport? Provide your solution process. | We will apply the principle of inclusion-exclusion to find out the percentage of students playing at least one sport:
1. Let S represent the students who play soccer and B represent those who play basketball.
2. From the data provided:
P(S) = 25% of 240 = 0.25 * 240 = 60 students.
P(B) = 15% of 240 = 0.15 * 240 ... |
0.05 | In a family, there are 6 siblings. Each sibling has 4 cousins. If none of the cousins are siblings to each other, how many total children are there in the family including the cousins? Explain your reasoning. | Let's analyze the information step-by-step:
1. We start with 6 siblings in the family.
2. Each sibling has 4 cousins. Since no cousins are siblings to each other, the number of unique cousins remains constant regardless of how many siblings refer to them.
3. Thus, if there are 6 siblings and they share the same 4 cous... |
0.05 | A restaurant offers a special where you can choose 2 appetizers, 3 main courses, and 1 dessert. If there are 5 appetizers, 7 main courses, and 4 desserts available, how many different meal combinations can you create? Show your calculation process. | To find the total number of meal combinations, we need to calculate the combinations for each course separately and then multiply them together:
1. For appetizers, we need to choose 2 out of 5. The number of ways to choose k items from n is given by the combination formula C(n, k) = n! / [k!(n-k)!].
So, for appetiz... |
0.05 | A group of friends decided to pool their money to buy concert tickets. If they collectively raised $600 and each ticket costs $75, how many tickets can they purchase? Include your working steps. | To determine how many concert tickets the group can purchase, we follow these steps:
1. First, we note the total amount of money raised, which is $600.
2. Next, we identify the cost of each ticket, which is $75.
3. To find the number of tickets they can buy, we divide the total money by the price of one ticket:
Num... |
0.05 | A farmer has a certain number of apples. He gives away 20% of his apples to a friend and then sells 30% of the remaining apples at the market. If he originally had 200 apples, how many apples does he have left after these transactions? Show your work. | Let's break this down step-by-step:
1. The farmer starts with 200 apples.
2. First, he gives away 20% of his apples to a friend. To find out how many apples that is, we calculate:
Apples given away = 20% of 200 = 0.20 * 200 = 40 apples.
3. After giving away 40 apples, the number of apples he has left is:
... |
0.05 | In a class of students, 60% are girls. If there are 24 boys in the class, how many students are there in total? Provide your reasoning. | To solve this problem, let's analyze it step by step:
1. Let the total number of students in the class be represented as 'x'.
2. According to the information provided, 60% of the students are girls. This means that 40% of the students are boys (since 100% - 60% = 40%).
3. We know that there are 24 boys in the class, w... |
0.05 | If a company produces 150 gadgets in an hour and operates for 8 hours a day, but one day they only produced 80% of their usual output due to a machine malfunction, how many gadgets did they produce that day? Explain your calculations. | Let’s go through the calculation step-by-step:
1. The normal production rate of the company is 150 gadgets per hour.
2. They operate for 8 hours a day, so normally they would produce:
Normal daily production = Production rate * Hours worked = 150 gadgets/hour * 8 hours = 1200 gadgets.
3. However, on the day of... |
0.05 | A book club has 15 members. Each member reads 4 books each month. If 5 new members join the club next month, how many books will all members read together in that month? Show your steps clearly. | Let’s reason through this problem:
1. Currently, there are 15 members in the book club, and each member reads 4 books per month.
2. The total number of books read by the current members is:
Books read by current members = Number of members * Books per member = 15 * 4 = 60 books.
3. Next month, 5 new members wi... |
0.05 | A store offers a discount of 25% on a jacket that originally costs $80. If a customer buys two jackets during a sale, what is the total amount spent after applying the discount? Include your calculations. | Let’s calculate the total cost step-by-step:
1. The original price of one jacket is $80.
2. The discount offered is 25%. To find the discount amount, we calculate:
Discount amount = 25% of $80 = 0.25 * 80 = $20.
3. Now, we determine the sale price of one jacket after applying the discount:
Sale price = ... |
0.05 | A restaurant serves a special dish that requires 3 main ingredients. If the chef uses 50 grams of ingredient A, 75 grams of ingredient B, and 100 grams of ingredient C, what is the total weight of the ingredients used in making the dish? Show your work. | Let’s add up the weights of the ingredients step-by-step:
1. Ingredient A weighs 50 grams.
2. Ingredient B weighs 75 grams.
3. Ingredient C weighs 100 grams.
4. To find the total weight of all ingredients combined, we simply add them together:
Total weight = Weight of A + Weight of B + Weight of C = 50g + 75g ... |
0.05 | A student scored 85% on her first exam and 90% on her second exam. If both exams are weighted equally, what is her average score across the two exams? Provide your reasoning. | Let’s calculate the average score step-by-step:
1. The student's score on the first exam is 85%.
2. The student's score on the second exam is 90%.
3. To find the average score, we sum the scores and divide by the number of exams:
Average score = (Score on Exam 1 + Score on Exam 2) / Number of Exams.
4. Pluggi... |
0.05 | A family spends 30% of their monthly income on housing, 20% on food, and 10% on transportation. If their total monthly income is $4000, how much do they spend on each category? Calculate and explain your answer. | Let’s break down the expenses step-by-step:
1. The family's total monthly income is $4000.
2. For housing, they spend 30% of their income:
Housing expense = 30% of $4000 = 0.30 * 4000 = $1200.
3. For food, they spend 20% of their income:
Food expense = 20% of $4000 = 0.20 * 4000 = $800.
4. For transpor... |
0.05 | A scientist conducts an experiment where she measures the temperature of water every hour for 6 hours. The temperatures recorded are 22°C, 23°C, 21°C, 24°C, 22°C, and 23°C. What is the average temperature over the 6-hour period? Show your calculations. | Let’s calculate the average temperature step-by-step:
1. The temperatures recorded over the 6 hours are: 22°C, 23°C, 21°C, 24°C, 22°C, and 23°C.
2. To find the average temperature, we first sum all the recorded temperatures:
Total temperature = 22 + 23 + 21 + 24 + 22 + 23 = 135°C.
3. Now, we divide the total t... |
0.05 | A farmer has a certain number of sheep and cows. If the total number of legs among all the animals is 56, how many sheep and cows does he have if there are twice as many sheep as cows? Show your work. | Let's denote the number of cows as C and the number of sheep as S. According to the problem, we know that:
1. The total number of legs from both sheep and cows is 56.
2. Each cow has 4 legs and each sheep also has 4 legs.
3. There are twice as many sheep as cows, so S = 2C.
Now, let's express the total number of legs... |
0.05 | In a group of friends, everyone shakes hands with every other person exactly once. If there are 10 people in the group, how many handshakes occur? Explain your reasoning step-by-step. | To determine the total number of handshakes when each person shakes hands with every other person exactly once, we can use combinatorial mathematics.
1. When one person shakes hands with another, it counts as one handshake. Therefore, we need to count combinations of pairs of people.
2. The formula for finding the num... |
0.05 | A man has three times as much money as his friend. Together they have $240. How much money does each person have? Provide your reasoning. | Let’s denote the amount of money the friend has as F. Since the man has three times as much money as his friend, we can represent the man's money as 3F.
1. According to the problem, together they have $240, which gives us the equation:
F + 3F = 240.
2. Combining like terms results in:
4F = 240.
3. To find F, divide bo... |
0.05 | There are two boxes containing marbles. Box A contains 3 red and 5 blue marbles, while Box B contains 2 red and 6 blue marbles. If you randomly select one marble from each box, what is the probability that both marbles selected are blue? Show your calculations. | To find the probability that both marbles selected are blue, we first need to determine the total number of marbles in each box and the probabilities of selecting a blue marble from each box.
1. In Box A, there are 3 red and 5 blue marbles, giving a total of:
Total in Box A = 3 + 5 = 8 marbles.
Probability of selecting... |
0.05 | A family has a dog and a cat. The dog weighs twice as much as the cat. If the combined weight of the dog and cat is 36 pounds, what is the weight of each pet? Show your steps clearly. | Let’s denote the weight of the cat as C pounds. Then, according to the problem, the weight of the dog would be 2C pounds because the dog weighs twice as much as the cat.
1. The combined weight of the dog and cat is given as 36 pounds, leading to the equation:
C + 2C = 36.
2. Combining like terms gives:
3C = 36.
3. To f... |
0.05 | A class consists of boys and girls. If there are 12 more boys than girls and the total number of students in the class is 36, how many boys and girls are there? Provide your reasoning step-by-step. | Let’s denote the number of girls in the class as G. According to the problem, the number of boys can be expressed as B = G + 12, since there are 12 more boys than girls.
1. The total number of students in the class is given as 36, leading to the equation:
G + B = 36.
2. Substituting B with (G + 12) into the equation gi... |
0.05 | In a certain city, 60% of the population are adults. If the adult population is 30,000, what is the total population of the city? Show your work clearly. | Let’s denote the total population of the city as P. We know that 60% of the population are adults, which means:
0.60P = 30,000.
1. To find P, we can rearrange the equation:
P = 30,000 / 0.60.
2. Performing the division gives:
P = 50,000.
Thus, the total population of the city is 50,000. |
0.05 | A store sells pencils at 25 cents each and erasers at 75 cents each. If a student buys a total of 10 items and spends $5, how many pencils and erasers did the student buy? Include your reasoning. | Let’s denote the number of pencils bought as P and the number of erasers as E. We know two things:
1. The total number of items purchased is 10, which gives us the equation:
P + E = 10.
2. The total cost spent on these items is $5, or 500 cents, leading to the equation:
25P + 75E = 500.
Now we have a system of equatio... |
0.05 | A farmer has a certain number of apples. He gives away 30% of his apples to his neighbor and then sells 50% of the remaining apples at the market. If he ends up with 140 apples, how many apples did he start with? Show your work. | Let's denote the initial number of apples as x.
1. The farmer gives away 30% of his apples:
Apples given away = 0.3 * x.
2. After giving away these apples, the number of apples left is:
Remaining apples = x - (0.3 * x) = 0.7 * x.
3. Next, he sells 50% of the remaining apples:
Apples sold = 0.5 * (0.7 * x) = ... |
0.05 | In a class of students, 60% are girls. If there are 24 boys in the class, how many students are there in total? Provide step-by-step reasoning. | Let the total number of students be denoted as y.
1. Since 60% of the students are girls, it follows that 40% must be boys (100% - 60%).
2. We can express the number of boys mathematically as:
Number of boys = 0.4 * y.
3. According to the problem, there are 24 boys:
0.4 * y = 24.
4. To solve for y, we divide bot... |
0.05 | If a rectangle's length is twice its width and the perimeter is 48 cm, what are the dimensions of the rectangle? Explain your steps clearly. | Let the width of the rectangle be w cm. Then the length will be 2w cm.
1. The formula for the perimeter P of a rectangle is:
P = 2(length + width).
2. Substituting the known values into the formula:
48 = 2(2w + w).
3. Simplifying the equation:
48 = 2(3w) = 6w.
4. Now, divide both sides by 6 to find w:
w = ... |
0.05 | Three friends, Alice, Bob, and Charlie, have some marbles. Alice has twice as many marbles as Bob, and Bob has three times as many marbles as Charlie. If Charlie has 10 marbles, how many marbles do all three friends have together? Show your calculations. | Let C represent the number of marbles Charlie has, which is given as 10.
1. From the information provided, Bob has three times as many marbles as Charlie:
B = 3C = 3 * 10 = 30.
2. Alice has twice as many marbles as Bob:
A = 2B = 2 * 30 = 60.
3. Now, we can calculate the total number of marbles:
Total = A + B ... |
0.05 | A bookstore had a sale where each book was priced at $15. During the sale, they sold 80 books. However, if they had not offered the discount, they would have sold only 50 books. How much revenue did the bookstore generate during the sale compared to potential revenue without the sale? Calculate and explain your finding... | 1. First, let's calculate the revenue generated during the sale:
Revenue from sale = Price per book * Number of books sold = $15 * 80 = $1200.
2. Now, let's calculate the potential revenue without the sale:
Potential revenue = Price per book * Number of books sold without discount = $15 * 50 = $750.
3. Finally, w... |
0.05 | A car travels through three different cities. The distance between city A and city B is 150 miles, while the distance between city B and city C is 200 miles. If the car averages 60 miles per hour on the first leg of the trip and 75 miles per hour on the second leg, how long does the entire trip take? Show your calculat... | 1. First, we need to calculate the time taken to travel from city A to city B:
Time from A to B = Distance / Speed = 150 miles / 60 mph = 2.5 hours.
2. Next, we calculate the time taken to travel from city B to city C:
Time from B to C = Distance / Speed = 200 miles / 75 mph = 2.67 hours (approximately).
3. Now, ... |
0.05 | In a family, the ratio of the ages of the father to the son is 5:2. If the father's age is currently 45 years, how old is the son? Provide detailed reasoning. | Let F represent the father's age and S represent the son's age.
1. We know from the problem that the ratio of their ages is 5:2:
F/S = 5/2.
2. Given that the father's current age is 45 years, we substitute F:
45/S = 5/2.
3. Cross-multiplying gives us:
5S = 90.
4. Now, dividing both sides by 5 yields:
S = 9... |
0.05 | A factory produces gadgets. In one week, it produced 240 gadgets. If production increases by 25% in the next week, how many gadgets will the factory produce in that week? Show your calculations step-by-step. | 1. Let's determine the increase in production:
Increase = 25% of 240 = 0.25 * 240 = 60 gadgets.
2. Now, we add this increase to the original production to find the new total:
New production = Original production + Increase = 240 + 60 = 300 gadgets.
Therefore, the factory will produce 300 gadgets in the following... |
0.05 | A group of friends decides to split the cost of a dinner bill evenly. If the total bill is $180 and there are 12 friends, how much does each friend pay? Provide a clear breakdown of your calculation. | 1. To find out how much each friend pays, we divide the total bill by the number of friends:
Amount per friend = Total bill / Number of friends = $180 / 12.
2. Performing the division gives:
Amount per friend = $15.
Thus, each friend pays $15. |
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