Question

In a swimming club, the ratio of girls to boys is 5:3. After 3 more girls and 5 more boys joined the club this spring, the ratio became 7:5. How many boys and girls total were in the club before spring

Answer 1

15 boys, 25 girls

Explanation:

Let x be a multiplier such that there are 5x girls and 3x boys before spring. This makes the girl : boy ratio be 5x : 3x = 5 : 3.

Then after spring, we have ...

(5x +3) / (3x +5) = 7/5

5(5x +3) = 7(3x +5) . . . . . "cross multiply"

25x +15 = 21x +35 . . . . . eliminate parentheses

4x = 20 . . . . . . . . . . . . . . subtract 21x+15

x = 5 . . . . . . . the multiplier is 5

So, the numbers of girls and boys before spring were ...

5x girls = 5·5 girls = 25 girls

3x boys = 3·5 boys = 15 boys