Question
Two years after a couple's marriage, a son was born.
Four years after the son's birth, the average age of the family is 28 years. Six years later, the sum of ages of the mother and son will be 64 years. Find the age of the father at the time of marriage.Solution
Let father's age at marriage = x, mother's = y 6 years after marriage, family (father, mother, 4-year-old son) has average age = 28 Total age = 28 × 3 = 84 x+y+16 = 84 → x + y = 68 → (1) 6 years later (i.e. 12 years after marriage), son is 10, mother's age = y+12 Given: mother + son = 64 y+12+10=64 → y = 42 Plug into (1): x+42 = 68 → x = 26
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