Chapter 9.3, Problem 48STP

a.

To determine

To write the expression for the share of the profits each nonsales manager.

Answer to Problem 48STP

  $\frac{5}{100}\left(\frac{8}{100}\cdot \frac{1}{6}\right)p+\left(\frac{50}{100}\right)\left(\frac{8}{100}\cdot \frac{1}{4}\right)p$

Explanation of Solution

Given:

It is provided that $5\%$ of, $8\%$ of the corporation's profits will be divided equally among all six managers.

Calculation:

Assume p represents the profits, then the share of profits each non sales manager will receive is,

  $\frac{5}{100}\left(\frac{8}{100}\cdot \frac{1}{6}\right)p$

Similarly, each nonsales manager's share of profit, when the rest $50\%$ is split among four nonsales manager, is,

  $\left(\frac{50}{100}\right)\left(\frac{8}{100}\cdot \frac{1}{4}\right)p$

The share of the profits each nonsales manager will receive is,

  $\frac{5}{100}\left(\frac{8}{100}\cdot \frac{1}{6}\right)p+\left(\frac{50}{100}\right)\left(\frac{8}{100}\cdot \frac{1}{4}\right)p$

b.

To determine

To simplify the expression.

Answer to Problem 48STP

  $\frac{p}{60}$ .

Explanation of Solution

Given:

It is provided that $5\%$ of, $8\%$ of the corporation's profits will be divided equally among all six managers.

Calculation:

The expression in part (a) is simplified as follows.

  $\begin{array}{l}\frac{5}{100}\left(\frac{8}{100}\cdot \frac{1}{6}\right)p+\left(\frac{50}{100}\right)\left(\frac{8}{100}\cdot \frac{1}{4}\right)p\\ =\frac{p}{150}+\frac{p}{100}\\ =\frac{5p}{300}\\ =\frac{p}{60}\end{array}$

Therefore, simplified expression is $\frac{p}{60}$ .

c.

To determine

To write and simplify the expression for the share of the profits each sales manager.

Answer to Problem 48STP

  $\frac{p}{150}$

Explanation of Solution

Given:

It is provided that $5\%$ of, $8\%$ of the corporation's profits will be divided equally among all six managers.

Calculation:

Similarly, each sales manager's share of the profits will be,

  $\frac{5}{100}\left(\frac{8}{100}\cdot \frac{1}{6}\right)p$

Simplify the expression.

  $\begin{array}{l}\frac{5}{100}\left(\frac{8}{100}\cdot \frac{1}{6}\right)p\\ =\frac{p}{150}\end{array}$

Therefore, the share of profits each sales manager will receive is $\frac{p}{150}$ .