Multiple choice

The average age of a father, a mother and a daughter is 39 years. What is the age of the father if the mother's age is 5 years less than that of the father and 1 year more than double the age of the daughter?

  1. 45 years

  2. 22 years

  3. 42 years

  4. 50 years

  5. 55 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the father's age be F. Mother's age is F - 5. Daughter's age is (F - 5 - 1) / 2 = (F - 6) / 2. The average age is (F + F - 5 + (F - 6) / 2) / 3 = 39. Solving for F: 2F - 5 + 0.5F - 3 = 117, so 2.5F = 125, giving F = 50.

AI explanation

Let the father's age be F, making the mother's age F - 5. Because the mother is 1 year more than double the daughter's age, the daughter's age is ((F - 5) - 1) / 2, which simplifies to 0.5F - 3. The average formula gives F + (F - 5) + (0.5F - 3) = 117, so combining terms results in 2.5F = 125. Solving this linear equation gives the father's age as 50 years.

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