BTGmoderatorDC wrote: ↑

Tue Feb 11, 2020 1:50 am

The ratio of men to women in a class is 6 to 5. If 2 men and 1 woman drop out of the class and the ratio of men to women after the drop out is 8 to 7, then how many men are currently in the class?

A. 14
B. 16
C. 18
D. 20
E. 22


OA C

Source: Princeton Review

Let men be \(m\) and women be \(w\) in the class

\begin{align*}
\dfrac{m}{w} &= \dfrac{6}{5} \\
5m &= 6w.
\end{align*}
Then
\begin{align*}
\dfrac{m-2}{w-1} &= \dfrac{8}{7} \\
7(m-2) &= 8(w-1) \\
7m - 14 &= 8w - 8 \\
7m - 6 &= 8\cdot \dfrac{5m}{6} \\
7m - 6 &= \dfrac{20m}{3} \\
21m - 18 &= 20m \\
m &= 18.
\end{align*}
Therefore, __C__