Chapter 7.2, Problem 42E

(a)

To determine

To Estimate: How many months you must purchase a membership for the average cost per month to fall to $\$69$ .

Answer to Problem 42E

  $10$ months

Explanation of Solution

Given: To join a rock climbing gym you must pay an initial fee of $\$100$ and a monthly fee of $\$59$

According to the data

Let $c$ be the cost and $m$ be the months

The equation becomes

  $c=\frac{59m+100}{m}$

Solving when cost per month to fall to $\$69$ .

i.e.

  $\begin{array}{l}c=\frac{59m+100}{m}\\ 69=\frac{59m+100}{m}\\ 69m=59m+100\\ 60m-59m=100\\ m=10\end{array}$

Hence, $10$ months.

(b)

To determine

To Find: What happens to the average cost as the number of months that you are a member increases.

Answer to Problem 42E

As the month increases, average cost decreases.

Explanation of Solution

Given: To join a rock climbing gym you must pay an initial fee of $\$100$ and a monthly fee of $\$59$

  $\begin{array}{l}c=\frac{59m+100}{m}\\ c=\frac{59m}{m}+\frac{100}{m}\\ c=59+\frac{100}{m}\end{array}$

As the month increases, average cost decreases