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A total of 22 men and 26 women were at a party, and the aver

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Carcass
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A total of 22 men and 26 women were at a party, and the aver [#permalink] New post   10 Sep 2020, 11:02
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A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33
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Re: A total of 22 men and 26 women were at a party, and the aver [#permalink] New post   10 Sep 2020, 11:03
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Re: A total of 22 men and 26 women were at a party, and the aver [#permalink] New post   13 Sep 2020, 08:59
sum of ages of adults in the party =48*35=1680

sum of ages of men in party =22*38=836

sum of ages of womenin party =1680-836=844

average age of women in party= 844/26=32.46=32.5

answer will be D
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Re: A total of 22 men and 26 women were at a party, and the aver [#permalink] New post   14 Sep 2020, 10:39
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Carcass wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

There are 48 people in total.
So, 22/48 = the proportion of women
And 26/48 = the proportion of men

Let x = average age of the women

So, plugging the information into the formula, we get: (22/48)(38) + (26/48)(x) = 35
Simplify: (11/24)(38) + (13/24)(x) = 35
Multiply both sides by 24 to get: (11)(38) + 13x = (35)(24)
Simplify: 418 + 13x = 840
Rearrange: 13x = 422
Solve: x = 422/13 ≈ 32.5

Answer: D

Cheers,
Brent
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Re: A total of 22 men and 26 women were at a party, and the aver [#permalink] New post   23 Aug 2022, 01:18
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