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 womenAnd
26/48 = the proportion of menLet
x = average age of the womenSo, 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
_________________
Brent Hanneson - founder of Greenlight Test Prep