Chapter 4.1, Problem 32PPS

a.

To determine

The equation that represents the total cost of the membership.

Answer to Problem 32PPS

The equation that represents the total cost of the membership is $y=5x+265$ .

Explanation of Solution

Given: It is given that a local recreation center offers a yearly membership of $265 and an additional $5 per class for aerobic classes.

Calculation:

Considering that the number of aerobic classes are $\left(x\right)$ in number and the total cost of the membership is $\left(y\right)$ . Also, the yearly membership is $265 and an additional $5 per class for aerobic classes. Therefore, using the linear regression model, the total cost of the membership is written as,

  $y=5x+265$

b.

To determine

If Carly spend $500 in a year then how many aerobic classes did she take.

Answer to Problem 32PPS

The number of aerobics are 47.

Explanation of Solution

Given: It is given that a local recreation center offers a yearly membership of $265 and an additional $5 per class for aerobic classes.

Calculation:

Considering that the number of aerobic classes are $\left(x\right)$ in number and the total cost of the membership is $\left(y\right)$ . Also, the yearly membership is $265 and an additional $5 per class for aerobic classes. Therefore, using the linear regression model, the total cost of the membership is written as,

  $y=5x+265$

Now, the number of aerobic classes are $\left(x\right)$ in number and the total cost of the membership is $\left(y\right)$ . Therefore, according to question, if the total cost is $500, then the number of aerobics are evaluated from (1) as,

  $\begin{array}{c}500=5x+\mathrm{265......}\left(\text{Plugging for }y=500\right)\\ 5x=235\\ x=47\end{array}$