Henry Ernest Dudeney/Puzzles and Curious Problems/5 - Dividing the Legacy/Solution

by : $5$

 * Dividing the Legacy
 * A man left $\pounds 100$ to be divided between his two sons Alfred and Benjamin.
 * If one-third of Alfred's legacy be taken from one-fourth of Benjamin's, the remainder would be $\pounds 11$.


 * What was the amount of each legacy?

Solution
Alfred gets $\pounds 24$ and Benjamin gets $\pounds 76$.

Proof
Let $A$ and $B$ be the amount of Alfred's and Benjamin's legacies respectively.

We have: