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Weighted Average problem

This topic has 3 expert replies and 1 member reply

Weighted Average problem

Post Sat Jul 22, 2017 1:46 am
A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number of tickets sold by the male members of the association

A. 50
B. 56
C. 58
D. 62
E. 66

The women's differential multiplied by 2 will cancel with the men's differential multiplied by 1. If the men's differential is m, then:

1*m + 2*(+4) = 0
m + 8 = 0
m = - 8

The men sold an average of 8 fewer tickets than the total average: 66 - 8 = 58.

Hello,

Could you please further explain why the 1*m+2*4 must offset so that we can find m = -8?

Many thanks

Regards

Anna

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agrineer Newbie | Next Rank: 10 Posts Default Avatar
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Post Sun Aug 20, 2017 9:23 am
male to female is 1:2
1*m+2*f
1*m+2*70=198~~66is avg for 1, so 3*66=198
m=198-140
m=58

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Post Sun Aug 06, 2017 10:49 pm
We could do it algebraically too, though I like the conceptual approach better.

Let's call m the male average and f the female average. We know that the total number of tickets can be represented in two ways:

(Average) * (# of People)

OR

(Female Average) * (# of Women) + (Male Average) * (# of Men)

Since these represent the same number, they must be equal:

66 * (m + w) = x * m + 70 * w

We know that w = 2m, so we can replace w with 2m:

66 * (m + 2m) = x * m + 70 * 2m

198m = xm + 140m

58m = xm

58 = x

and we're done! Smile

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agrineer Newbie | Next Rank: 10 Posts Default Avatar
Joined
20 Oct 2009
Posted:
1 messages
Post Sun Aug 20, 2017 9:23 am
male to female is 1:2
1*m+2*f
1*m+2*70=198~~66is avg for 1, so 3*66=198
m=198-140
m=58

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Matt@VeritasPrep GMAT Instructor
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625
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Post Sun Aug 06, 2017 10:49 pm
We could do it algebraically too, though I like the conceptual approach better.

Let's call m the male average and f the female average. We know that the total number of tickets can be represented in two ways:

(Average) * (# of People)

OR

(Female Average) * (# of Women) + (Male Average) * (# of Men)

Since these represent the same number, they must be equal:

66 * (m + w) = x * m + 70 * w

We know that w = 2m, so we can replace w with 2m:

66 * (m + 2m) = x * m + 70 * 2m

198m = xm + 140m

58m = xm

58 = x

and we're done! Smile

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