At a charity carnival, the ratio of the number of adults to the number of children is 2 : 5. Among the children, the ratio of the number of girls to the number of boys is 3 : 5. A total of 1392 game tickets are given out. Each adult receives 4 tickets and each child receives 10 tickets. How many tickets are given to the boys?
Question
At a charity carnival, the ratio of the number of adults to the number of children is 2 : 5. Among the children, the ratio of the number of girls to the number of boys is 3 : 5. A total of 1392 game tickets are given out. Each adult receives 4 tickets and each child receives 10 tickets. How many tickets are given to the boys?
Solution
Step 1: Determine the total number of adults and children at the carnival.
We know that the ratio of adults to children is 2:5 and that each adult receives 4 tickets and each child receives 10 tickets. We can set up the following equation to represent the total number of tickets given out:
4(2x) + 10(5x) = 1392
Solving this equation gives us the value of x:
8x + 50x = 1392 58x = 1392 x = 1392 / 58 x = 24
Step 2: Determine the number of children at the carnival.
We know that the ratio of adults to children is 2:5, so the number of children at the carnival is 5x:
5 * 24 = 120 children
Step 3: Determine the number of boys among the children.
We know that the ratio of girls to boys among the children is 3:5, so the number of boys is 5/8 of the total number of children:
5/8 * 120 = 75 boys
Step 4: Determine the number of tickets given to the boys.
We know that each child receives 10 tickets, so the number of tickets given to the boys is:
10 * 75 = 750 tickets
So, 750 tickets are given to the boys.
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