## 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 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.

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