A club sold an average (arithmetic mean) of 92 raffle tickets per memb

We can solve this question using weighted averages

Weighted 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 + 96M
Expand the left side of the equation: 92F + 92M = 84F + 96M
Subtract 92M from both sides of the equation: 92F = 84F + 4M
Subtract 84F from both sides of the equation: 8F = 4M

We 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 = 4M
Divide both sides by F to get: 8 = 4M/F
Divide both sides by 4 to get: 8/4 = M/F
Simplify: 2/1 = M/F

So, the ratio of the number of male members to the number of female members = 2 : 1

Answer: D

Male : Average : Female
96 : 92 : 84

92-84: 96-92
8:4
2:1
D

The average of 92 is closer to 96 (male) than 84 (female)
So there is more weightage on male number than female number which pulls the total average more towards Male average, so answer has to be D or E

using alligation: M:F = \(\frac{(Total average - Female average)}{(Male average - Total Average)}\) = \(\frac{(92-84)}{(96-92)}\)
=\(\frac{8}{4}\) = \(\frac{2}{1}\)

Answer D

We are given that a club sold an average (arithmetic mean) of 92 raffle tickets per member, that among the female members, the average number sold was 84, and that among the male members, the average number sold was 96. We can let f = the number of females and m = the number of males, and we can create the following weighted average equation:

92 = (84f + 96m)/(m + f)

92m + 92f = 84f + 96m

8f = 4m

2f = m

2 = m/f

Answer: D

Why isn't this M:F 1:2? I understand the average of the men's sold are higher but they want to know M;F ratio right? What am I missing?

The weighted avg is closer to the heavily weighted side. Here, since 92(weighted avg) is closer to 96 than 84, the number of males must be greater than women. Hence
M/F = (92-84)/(96-92) = 2/1

The average tickets sold per member (92) is closer to the average tickets sold to males (96) than it is to the average tickets sold to females (84). This means there must be more males than females to skew the overall average closer to the male average. The average tickets sold to males is 4 tickets more than the overall average, while the average tickets sold to females is 8 tickets less than the overall average. Therefore, there must be twice as many males as females.

Hope it's clear.