Henry Ernest Dudeney/Modern Puzzles/24 - Simple Arithmetic/Solution

by : $24$

 * "Simple" Arithmetic

Solution

 * $20$ and $64$.

Proof
Let their ages be $a$ and $b$.

Then:

You can either factorise $1280$ into its two factors which differ by $44$, which brings us no further than where we started from, or we use the Quadratic Formula to smash this exquisite gem with a mallet:


 * $b = \dfrac {-44 \pm \sqrt {44^2 + 4 \times 1280} } 2 = -22 \pm 42$

and we can pick out what we want from the debris.