# The profits of a business are shared among three stockholders

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:

**= first stockholder**

*x***= second stockholder**

*y***= third stockholder**

*z***+**

*x***+**

*y***= 26400 [Eq. 1]**

*z***= 2**

*x***[Eq. 2]**

*y***= 3**

*y***[Eq. 3]**

*z*Rewriting Eq. 3 in terms of

**will give:***z***= 3**

*y***[Eq. 3]**

*z***/3 =**

*y*

*z***=**

*z***/3 [Eq. 4]**

*y*Now, we can solve the

**of***value***by using Eq. 1 substituting the known values for***y***and***x***as follows:***z***+**

*x***+**

*y***= 26400 [Eq. 1]**

*z* (2

**) +***y***+ (***y***/3) = 26400***y* 3

**+***y***/3 = 26400***y* 3[3

**+***y***/3] = [26400]3***y* 9

**+***y***= 79200***y* 10

**= 79200***y***= 79200/10**

*y***= 7920**

*y*Using Eq. 2, we can derive the value of

**:***x***= 2y [Eq. 2]**

*x***= 2(7920)**

*x***= 15840**

*x*Using Eq. 1, we can solve for the value

**:***z***+**

*x***+**

*y***= 26400 [Eq. 1]**

*z*15840 + 7920 +

**= 26400***z*23760 +

**= 26400***z***= 26400 – 23760**

*z***= 2640**

*z*Therefore, there first stockholder receives 15,840 dollars, the second stockholder receives 7,920 dollars and the third stockholder receives 2,640 dollars.

**Check:**

**+**

*x***+**

*y***= 26,400 [Eq. 1]**

*z*[

*The sum of the profits of the 3 stockholders is $26,400*]15,840 + 7,920 + 2,640 = 26,400

26,400 = 26,400

**= 2**

*x***[Eq. 2]**

*y*[

*The first stockholder’s profit is twice that of the second*]15,840 = 2(7,920)

15,840 = 15,840

**= 3**

*y***[Eq. 3]**

*z*[

*The second stockholder’s profit is three time that of the third*]7,920 = 3(2,640)

7,920 = 7,920