Chapter 8.1, Problem 35PPS

(a)

To determine

To Write: Equation that gives the total cost as a function of number of miles driven

Answer to Problem 35PPS

  $c(m)=0.55m+50$

Explanation of Solution

Given information: The rental company charges 50 for the truck and additional fee of 0.55 per mile driven.

Frame equation:Let $m$ be the number of miles driven and $c(m)$ be the total cost

Total cost = rate per mile times number of miles plus rental charge

The function to calculate the total cost is,

  $c(m)=0.55m+50$

(b)

To determine

To Calculate: The number of miles he drove the truck.

Answer to Problem 35PPS

Logan drove 142 miles

Explanation of Solution

Given information: The rental company charges 50 for the truck and additional fee of 0.55 per mile driven. The function for total cost is $c(m)=0.55m+50$ . Logan spends 128.10 to rent a truck.

Calculation:The function to calculate the total cost is,

  $c(m)=0.55m+50$

We need to find the number of miles driven $m$ . We know that Logan spends 128.10

Substitute 128.10 for $c(m)$ in the function and solve for $m$

  $\begin{array}{l}c(m)=0.55m+50\\ 128.10=0.55m+50\\ 128.10-50=0.55m+50-50\\ 78.1=0.55m\\ m=\frac{78.1}{0.55}=142\end{array}$

Logan drove 142 miles