Answer: 108
Step-by-step 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 [tex]\dfrac{2}{3}x[/tex]
and the number of men will be [tex]\dfrac{1}{4}x[/tex]
According to the question, we have
[tex]\dfrac{2}{3}x+\dfrac{1}{4}x+9=x\\\\\Rightarrow\ \dfrac{8x+3x}{12}+9=x\\\\\Rightarrow\ x-\dfrac{11}{12}x=9\\\\\Rightarrow\ \dfrac{12x-11x}{12}=9\\\\\Rightarrow\ x=12\times9=108[/tex]
Hence, the total number of faculty members = 108
Answer:
36
Step-by-step 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 $\frac{3}{4}\cdot \frac{1}{3}\cdot x=9\implies x=36$.
