mathschallenge.net

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

Therefore (9$n$+17)/10n=8/7, 7(9$n$+17)=810$n$, 63$n$+119=80$n$.

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

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