Chiu Chang Suann Jing/Examples/Example 3

Example of Problem from

 * A number of men bought a number of articles, neither of which are known;
 * it is only known that if each man paid $8$ cash, there would be a surplus of $3$ cash,
 * and if each man paid $7$ cash, there would be a deficiency of $4$ cash.


 * Required the respective numbers?

Solution
There are $7$ men and $53$ objects.

Proof
Let $m$ be the number of men.

Let $p$ be the number of objects.

It is assumed that the objects each cost $1$ cash each.

Then: