Mother and Daughter's Birthday Bicycle Deal
A twelve-year-old girl asks her mother for a bicycle. Her mother, who is forty-five, strikes a deal: she can have the bicycle exactly when the mother's age is three times the girl's own age. Assuming they both simply keep getting a year older at the same steady rate, how long must the girl wait?
Reveal the answer
4½ years — at that point the girl is 16½ and her mother is 49½, and 49½ is exactly three times 16½. It's Puzzle No. 45, 'Mother and Daughter,' from Henry Dudeney's 1917 Amusements in Mathematics; the twist is that the exact moment falls mid-year, not on a birthday.
— Henry Dudeney, Amusements in Mathematics — Puzzle No. 45, 'Arithmetical and Algebraical Problems,' 1917
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