Chapter 8.1, Problem 35PPS

(a)

To determine

To identify: the independent and dependent variables.

Answer to Problem 35PPS

The required function is $c\left(s\right)=50+0.55s$ .

Explanation of Solution

Given:

Spent $128.10 to rent a truck

Rental Company charges - $50 An additional fee of $0.55 per mile

Calculation:

Let c be the total cost and s be the total number of miles

Since the total cost depends on the number of miles that he drives, total cost c be the dependent variable and total number of miles s be the independent variable.

Words: $\text{Total cost}=\$50+\text{fee per mile times number of miles}$

Function: $c\left(s\right)=50+0.55s$

Conclusion: Therefore, the required function is $c\left(s\right)=50+0.55s$ .

(b)

To determine

To find: the number of miles that he drove the truck.

Answer to Problem 35PPS

The total number of miles that he drives the truck is 142

Explanation of Solution

Calculation:

Need to find the number of miles that he drives the truck

Consider the equation

  $c\left(s\right)=50+0.55s$

Substitute $c\left(s\right)=128.10$ in above equation

  $128.10=50+0.55s$

  $\begin{array}{l}128.10-50=0.55s\text{ Simplify}\\ \text{78}\text{.10=0}\text{.55}s\\ \frac{78.10}{0.55}=s\text{ Divide each side by 0}\text{.55}\\ \text{142=}s\end{array}$

Conclusion: Therefore, the total number of miles that he drives the truck is 142.