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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

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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

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If the ratio of men to women is 6 to 5, the number of men must be a multiple of 6. Only one answer is a multiple of 6, namely 18, so that has to be right.
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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__

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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
The ratio 6 : 5 can be re-expressed as 6x : 5x, where 6x is the number of men currently in the class and 5x is the number of women currently in the class.

We can create the equation:

(6x - 2) / (5x - 1) = 8/7

7(6x - 2) = 8(5x - 1)

42x - 14 = 40x - 8

2x = 6

x = 3

So, there are 6 * 3 = 18 men in the class.

Answer: C

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