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If 3/4 of the number of women working at Company X is equal to 2/3 of
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12 Jan 2021, 09:10
12 Jan 2021, 09:10
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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
Kudos for the right answer and explanation
A) 5/12
B) 8/17
C) 1/2
D) 7/12
E) 8/9
Kudos for the right answer and explanation
Re: If 3/4 of the number of women working at Company X is equal to 2/3 of
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12 Jan 2021, 09:25
12 Jan 2021, 09:25
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Let the fraction of men be M and that of women be W and the total number of employees be n
according to the question,
3Wn/4 = 2Mn/3
n can be divided from both sides.
since there are only men and woman in the company,
M+W=1
substituting in the equation above,
3W/4=2(1-W)/3
on simplifying,
W=8/17
according to the question,
3Wn/4 = 2Mn/3
n can be divided from both sides.
since there are only men and woman in the company,
M+W=1
substituting in the equation above,
3W/4=2(1-W)/3
on simplifying,
W=8/17
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Re: If 3/4 of the number of women working at Company X is equal to 2/3 of
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12 Jan 2021, 10:23
12 Jan 2021, 10:23
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Carcass 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
Kudos for the right answer and explanation
A) 5/12
B) 8/17
C) 1/2
D) 7/12
E) 8/9
Kudos for the right answer and explanation
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
