Chapter 4.2, Problem 32PPS

Solution

a.

The equation that represents the total cost of the membership.

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

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.

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

The number of aerobics are 47.

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,

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