Multiple choice

Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is

  1. $54$
  2. $72$
  3. $105$
  4. $108$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let F and S be current ages. (F-18) = 3(S-18) and F = 2S. Substituting F=2S into the first gives 2S-18 = 3S-54, so S=36 and F=72. Sum = 36+72 = 108.

AI explanation

Let the son's present age be s years and the father's present age be f years; we are given f equals 2s. Eighteen years ago, the father was 3 times as old as his son, so f minus 18 equals 3 times (s minus 18). Substituting 2s for f gives 2s minus 18 equals 3s minus 54, meaning s equals 36. The father's age is 2 times 36, or 72, and the sum of their present ages is 36 plus 72, which equals 108.

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