Henry Ernest Dudeney/Puzzles and Curious Problems/134 - The Bag of Nuts/Solution

by : $134$

 * The Bag of Nuts
 * There are $100$ nuts distributed between $5$ bags.
 * In the first and second there are altogether $52$ nuts;
 * in the second and third there are $43$;
 * in the third and fourth there are $34$;
 * in the fourth and fifth, $30$.


 * How many nuts are there in each bag?

Proof
Let $a$, $b$, $c$, $d$ and $e$ be the number of nuts in each of the first, second, third, fourth and fifth bags respectively.

We have: