The mother, the child, and the missing father

Question

A mother is 21 years older than her child. In exactly six years she will be exactly five times as old as the child. Where is the father? This looks like an ordinary age puzzle with an oddly worded question. Do the algebra and take the answer seriously.

Accepted Answer

The child's age comes out as minus three quarters of a year: the child has not been born yet and is due in nine months. So the father is with the mother, and rather recently was even closer. The algebra. Let the child's age now be c years; the mother's age is c + 21. In six years the child is c + 6 and the mother is c + 27. Five times the child's age equals the mother's: 5(c + 6) = c + 27, so 5c + 30 = c + 27, so 4c = minus 3, so c = minus 3/4. Reading the answer. A "current age" of minus 3/4 of a year means the child will be born nine months from now. The puzzle's numbers are consistent: in …

The mother, the child, and the missing father

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