mathschallenge.net logo

Disco Ratios

Problem

The ratio of boys to girls at a school disco is 9:10.

An extra 17 boys arrive and the ratio changes to 8:7.

How many girls are there at the disco?


Solution

Originally there were 9n boys and 10n girls. With an extra 17 boys, we have 9n+17 boys and we know the ratio changes to 8:7.

Therefore (9n+17)/10n=8/7, 7(9n+17)=8times10n, 63n+119=80n.

Solving this, 17n=119, hence n=7.

So we can determine that there are 10n=70 girls at the disco.

Problem ID: 131 (Nov 2003)     Difficulty: 2 Star

Only Show Problem