Henry Ernest Dudeney/Puzzles and Curious Problems/135 - Distributing Nuts

Puzzles and Curious Problems by Henry Ernest Dudeney: $135$

Distributing Nuts

Aunt Martha bought some nuts.

She gave Tommy one nut and a quarter of the remainder;

Bessie then received one nut and a quarter of what were left;

Bob, one nut and a quarter of the remainder;

and, finally, Jessie received one nut and a quarter of the remainder.

It was then noticed that the boys had received exactly $100$ nuts more than the girls.

How many nuts had Aunt Martha retained for her own use?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $135$. -- Distributing Nuts
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $208$. Distributing Nuts