Question

In a certain school, 2/3 of the faculty are women, 1/4 of the men on the faculty are married and the other 9 men are bachelors. How many faculty members are there?

Answer 1

36

Explanation:

Let there be $x$ faculty members. Then we have:

$x=\frac{2x}{3}+\frac{1}{4}\cdot \frac{x}{3}+9=\frac{3x}{4}+9\implies \frac{x}{4}=9\implies x=\boxed{36}$.

There is another way to think about the problem. We know that $\frac{3}{4}$ of $\frac{1}{3}$ of the faculty (the men) are the $9$ bachelors. Thus $\frac{3}{4}\cdot \frac{1}{3}\cdot x=9\implies x=36$.

Answer 2

Answer: 108

Explanation:

Given : In a certain school, 2/3 of the faculty are women, 1/4 of the men on the faculty are married and the other 9 men are bachelors.

Let x be the total number of faculty members, then the faculty women will be
`(2)/(3)x`

and the number of men will be
`(1)/(4)x`

According to the question, we have

`(2)/(3)x+(1)/(4)x+9=x\\\\\Rightarrow\ (8x+3x)/(12)+9=x\\\\\Rightarrow\ x-(11)/(12)x=9\\\\\Rightarrow\ (12x-11x)/(12)=9\\\\\Rightarrow\ x=12*9=108`

Hence, the total number of faculty members = 108