lalania1 wrote:
If 3/4 of the number of women working at Company X is equal to 2/3 of the number of men, what fraction of the employees at Company X are women?
A) 5/12
B) 8/17
C) 1/2
D) 7/12
E) 8/9
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 menWe 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 menLet 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 = MAside: 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 =
51/2So, 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
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