118. (Rule XXX). Two persons have equal capitals, each consisting of a known number of articles of equal value and a known number of coins. But both the number of articles and the sums of money are different for each. What is the value of the article?
118. Solution. Let the 1st have $a$ items and $m$ coins, and the 2nd have $b$ items and $p$ coins.

If $x$ is the value of an item, then $a x+m=b x+p$, from which

$$
x=\frac{p-m}{a-b}
$$

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