Bunuel wrote:
A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, average number sold was 84, and among the male members, the average number sold was 96. What was the ratio of the number of male members to the number of female members in the club?
(A) 1 : 1
(B) 1 : 2
(C) 1 : 3
(D) 2 : 1
(E) 3 : 1
We can solve this question using
weighted averagesWeighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...Let F = the number of female members
Let M = the number of male members
This means F + M = the TOTAL number of members.
Also, F/(F + M) = the proportion of female numbers, and M/(F + M) = the proportion of male numbers.
When we substitute the given values into the weighted averages formula, we get:
92 = F/(F + M)(84) + M/(F + M)(96)To eliminate the fractions, we'll multiply both sides of the equation by (F+M) to get:
92(F+M) = 84F + 96MExpand the left side of the equation:
92F + 92M = 84F + 96MSubtract 92M from both sides of the equation:
92F = 84F + 4MSubtract 84F from both sides of the equation:
8F = 4MWe want to determine the ratio of the number of male members to the number of female members in the club.
In other words, we want to find the value of M/F
So we'll take:
8F = 4MDivide both sides by F to get:
8 = 4M/FDivide both sides by 4 to get:
8/4 = M/FSimplify:
2/1 = M/FSo, the ratio of the number of male members to the number of female members = 2 : 1
Answer: D
_________________