If 3/4 of the number of women working at Company X is equal to 2/3 of

APPROACH #1: Two variables
Let w = # of women
Let m = # of men

3/4 of the number of women working at Company X is equal to 2/3 of the number of men
We can write: (3/4)w = (2/3)m
Rewrite as: 3w/4 = 2m/3
Cross multiply to get: 9w = 8m
Divide both sides of the equation by m to get: 9w/m = 8
Divide both sides of the equation by 9 to get: w/m = 8/9
This tells us that the ratio of women to men is 8 to 9.
In other words, for every 17 employees, 8 are women and 9 are men.
In other words, 8/17 of the employees are women.

Answer: B


APPROACH #2: One variable

Notice that the question does not ask us for the NUMBER of women; it asks us to determine the PROPORTION of women in the workforce.
In these instances, we can assign a certain value to the number of women, and then see what this implies about the number of men and then go from there.

Let say there are 12 women [12 is a nice value since it works with many of the values in the two given fractions]

3/4 of the number of women working at Company X is equal to 2/3 of the number of men
Let M = # of men
We can write: (3/4)(12) = (2/3)(M)
Simplify: 9 = (2/3)(M)
Multiply both sides by 3/2 to get: (3/2)(9) = M
Evaluate: 27/2 = M
Aside: Okay, so we get a fractional value for the number of men. No problem since we're supposed to answer the question....

What fraction of the employees at Company X are women?
Total number of employees = 12 + 27/2 = 24/2 + 27/2 = 51/2
So, the fraction of all employees who are women = 12/(51/2)
= 24/51 [multiplied top and bottom by 2]
= 8/17 [divided top and bottom by 3]
Answer: B