## 2410.21 – Tennis Team

A mixed tennis team of 12 persons has one-third women and two-thirds men. What is the smallest number of additional people that should be recruited so that the team as a whole is 20 percent women?

## Solution

At present there are 8 men and 4 women. Once we add x players, the women will be 20 percent, or 1/5. Since the women are now 33 1/3 percent, we will reduce their percentage by adding x men. Thus:

$\frac{8 + x}{12 + x} = \frac{4}{5} \rightarrow 4(12 + x) = 5(8 + x) \rightarrow 48 + 4x = 40 + 5x \rightarrow 8 = x.$

So 8 men must be recruited. (Why decrease the percentage of women in the first place?)