Henry Ernest Dudeney/Puzzles and Curious Problems/42 - Family Ages

Puzzles and Curious Problems by Henry Ernest Dudeney: $42$

Family Ages

A man and his wife had three children, John, Ben, and Mary,

and the difference between their parents' ages was the same as between John and Ben and between Ben and Mary.

The ages of John and Ben, multiplied together, equalled the age of the father,

and the ages of Ben and Mary multiplied together equalled the age of the mother.

The combined ages of the family amounted to ninety years.

What was the age of each person?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Age and Kinship Puzzles: $42$. -- Family Ages
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Age Puzzles: $37$. Family Ages