Question

A foreign language club at Washington Middle School consists of n students, 2/5 of whom are boys. All of the students in the club study exactly one foreign language. 1/3 of the girls in the club study Spanish and 5/6 of the remaining girls study French. If the rest of the girls in the club study German, how many girls in the club, in terms of n, study German?

Answer 1

Answer:

The number of girls in German club are $\frac{n}{15}$.

Step-by-step explanation:

Consider the provided information.

$\frac{2}{5}$ of n are boys.

Thus the number of girls are: $\frac{3n}{5}$.

1/3 of the girls in the club study Spanish.

Girls studying Spanish = $\frac{3n}{5}\times\frac{1}{3}=\frac{n}{5}$

That means now total number of girl left: $\frac{3n}{5}-\frac{n}{5}=\frac{2n}{5}$

5/6 of the remaining girls study French.

Girls studying French = $\frac{2n}{5}\times\frac{5n}{6}=\frac{n}{3}$

That means now total number of girl left: $\frac{2n}{5}-\frac{n}{3}=\frac{n}{15}$

The rest of the girls in the club study German.

Hence, the number of girls in German club are $\frac{n}{15}$.