Chapter 7.2, Problem 41E

(a)

To determine

To Estimate: How many students must use the program for the average cost per student to fall $\$30$ .

Answer to Problem 41E

  $50$

Explanation of Solution

Given: Your school purchases a math software program. The program has an initial cost of $\$500$ plus $\$20$ for each student that uses the program.

Let $x$ represents a number of students that are about to use the program.

Then

Cost of the program= $500+20x$

We want

  $\frac{500+20x}{x}=30$

Solving for $x$

  $\begin{array}{l}\frac{500+20x}{x}=30\\ 30x=500+20x\\ 30x-20x=500\\ 10x=500\\ x=50\end{array}$

  $50$ Students should use the program, average cost drops.

(b)

To determine

To Find: What happens to the average cost as more students use the program.

Answer to Problem 41E

Cost per student decreases

Explanation of Solution

Given: Your school purchases a math software program. The program has an initial cost of $\$500$ plus $\$20$ for each student that uses the program.

As more Students use the program, average cost drops

Because

  $\begin{array}{l}\frac{500+20x}{x}\\ \frac{500}{x}+20\\ y=20\\ \end{array}$

i.e.

Cost per student decreases.