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Bunuel
At a company, the average wage of male employees is $9.97 per hour, and the average wage of female employees is $10.37 per hour. If the average wage of all employees is $10.12 per hour, what is the ratio of the number of male employees to the number of female employees?

A) 1 to 2
B) 2 to 3
C) 3 to 2
D) 5 to 3
E) 2 to 1

Fact: Given two groups of people, A and B, if group A has an average of a and group B has an average of b and the overall average of the two groups is c, then the ratio of the number of people in group A to the number of people in group B is |b - c|/|a - c|.

Here, we can let group A be male employees and group B be female employees, so a = 9.97, b = 10.37 and c = 10.12. Since |b - c| = |10.37 - 10.12| = 0.25 and |a - c| = |9.97 - 10.12| = 0.15, the ratio of the number of male employees to the number of female employees is 0.25/0.15 = 25/15 = 5/3.

Alternate Solution:

We can let m = the number of male employees and f = the number of female employees. Using the weighted average formula, sum of weights/total = average, we have:

(9.97m + 10.37f) / (m + f) = 10.12

9.97m + 10.37f = 10.12m + 10.12f

0.25f = 0.15m

0.25/0.15 = m/f

5/3 = m/f

Answer: D
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At a company, the average wage of male employees is $9.97 per hour, and the average wage of female employees is $10.37 per hour. If the average wage of all employees is $10.12 per hour, what is the ratio of the number of male employees to the number of female employees?

A) 1 to 2
B) 2 to 3
C) 3 to 2
D) 5 to 3
E) 2 to 1
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