Profit Sharing

The profits of a business are shared among three stockholders. The first stockholder receives twice as much as the second and the second receives three times as much as the third. If the profits for last year were $26,400, how much did each stockholder receive?


Solution
This type of problem can be solved using equations in one variable only. This is possible since we can express one unknown value in terms of the other. Thus,

Let
        x = the share of the third stockholder
        3x = the share of the second stockholder $(3 \cdot x)$
        6x = the share of the first stockholder $(2 \cdot 3x )$

Hence, based on the problem statement, we can derive the following equation

        $x + 3x + 6x = 26400$

Solving for x yields

        $10x = 26400$
        $x = \frac{26400}{10} $
        $x = 2640$

Henceforth,

        $3x = 3(2640) = 7920 $
        $6x = 6(2640) = 15840 $

Therefore, the third stockholder received $2,640 share. The second stockholder received $7,920 share while the first stockholder received $15,840.

Check
Total share is $26,400: 2640 + 7920 + 15840 = 26,400