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

The number of girls in German club are
`(n)/(15)`.

Explanation:

Consider the provided information.

`(2)/(5)` of n are boys.

Thus the number of girls are:
`(3n)/(5)`.

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

Girls studying Spanish =
`(3n)/(5)*(1)/(3)=(n)/(5)`

That means now total number of girl left:
`(3n)/(5)-(n)/(5)=(2n)/(5)`

5/6 of the remaining girls study French.

Girls studying French =
`(2n)/(5)*(5n)/(6)=(n)/(3)`

That means now total number of girl left:
`(2n)/(5)-(n)/(3)=(n)/(15)`

The rest of the girls in the club study German.

Hence, the number of girls in German club are
`(n)/(15)`.