## A foreign language club at Washington Middle School consists of $$n$$ students, $$\dfrac25$$ of whom are boys. All of

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### A foreign language club at Washington Middle School consists of $$n$$ students, $$\dfrac25$$ of whom are boys. All of

by M7MBA » Thu Sep 17, 2020 12:55 am

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A

B

C

D

E

## Global Stats

A foreign language club at Washington Middle School consists of $$n$$ students, $$\dfrac25$$ of whom are boys. All of the students in the club study exactly one foreign language. $$\dfrac13$$ of the girls in the club study Spanish and $$\dfrac56$$ 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?

A. $$\dfrac{2n}5$$

B. $$\dfrac{n}3$$

C. $$\dfrac{n}5$$

D. $$\dfrac{2n}{15}$$

E. $$\dfrac{n}{15}$$

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### Re: A foreign language club at Washington Middle School consists of $$n$$ students, $$\dfrac25$$ of whom are boys. All o

by deloitte247 » Sun Sep 20, 2020 12:53 pm
$$Total\ number\ of\ \ students=n$$ \$
$$Total\ number\ of\ boys\ =\ \frac{2}{5}\ n$$
$$Number\ of\ girls=total\ students-boys$$
$$=\frac{1}{1}n-\frac{2}{5}n=\frac{5n-2n}{5}=\frac{3n}{5}$$
$$Number\ of\ girls\ studying\ \operatorname{span}ish\ =\ \frac{1}{3}\cdot\frac{3n}{5}=\frac{1n}{5}$$
$$Number\ of\ girls\ studying\ french\ =\ \frac{5}{6}of\ remaining\ girls$$
$$Number\ of\ remaining\ girls=\ \frac{3n}{5}-\frac{1n}{5}=\frac{2n}{5}$$
$$Therefore,\ number\ of\ girls\ studying\ french=\ \frac{5}{6}\cdot\frac{2n}{5}=\frac{1n}{3}$$
$$if\ the\ remaining\ girls\ study\ german,\ how\ many\ girls\ study\ german$$
$$total\ number\ of\ girls\ =\ girls\ studying\ \operatorname{span}ish\ +\ french\ +\ german$$
$$\frac{3n}{5}=\frac{1n}{5}+\frac{1n}{3}+number\ of\ girls\ studying\ german$$
$$number\ of\ girls\ studying\ german=\frac{3n}{5}-\frac{1n}{5}-\frac{1n}{3}$$
$$=\frac{9n-3n-5n}{15}$$
$$=\frac{1n}{15}or\ \frac{n}{15}$$
$$Answer\ =\ E$$

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### Re: A foreign language club at Washington Middle School consists of $$n$$ students, $$\dfrac25$$ of whom are boys. All o

by Scott@TargetTestPrep » Thu Sep 24, 2020 7:06 am
M7MBA wrote:
Thu Sep 17, 2020 12:55 am
A foreign language club at Washington Middle School consists of $$n$$ students, $$\dfrac25$$ of whom are boys. All of the students in the club study exactly one foreign language. $$\dfrac13$$ of the girls in the club study Spanish and $$\dfrac56$$ 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?

A. $$\dfrac{2n}5$$

B. $$\dfrac{n}3$$

C. $$\dfrac{n}5$$

D. $$\dfrac{2n}{15}$$

E. $$\dfrac{n}{15}$$