Multiple choice

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?

  1. $31$
  2. $31.5$
  3. $32$
  4. $32.5$
  5. $33$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total adults = 22 + 26 = 48. Total age = 48 * 35 = 1680. Men's total age = 22 * 38 = 836. Women's total age = 1680 - 836 = 844. Women's average = 844 / 26 = 32.46, which is closest to 32.5.

AI explanation

The total age for all 48 adults is 48 multiplied by 35, equaling 1680. The total age for the 22 men is 22 multiplied by 38, which is 836. Subtracting this from the overall total leaves the women with a combined age of 844. Dividing 844 by the 26 women gives an average age of exactly 32.46, which rounds to 32.5.

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