Chapter 3.1, Problem 49AYU

Truck Rentals A truck rental company rents a truck for one day by charging $\$39.95$ plus $\$0.89$ per mile.

a. Write a linear model that relates the cost $C$, in dollars, of renting the truck to the number $x$ of miles driven.

b. What is the cost of renting the truck if the truck is driven 110 miles? 230 miles?

To determine

To calculate:

a. Write a linear model that relates the cost $C$, in dollars, of renting the truck to the number of miles $x$ driven.

b.What is the cost of renting the truck if the truck is driven 110 miles? 230 miles?

Answer to Problem 49AYU

Solution:

a. $C(x)=0.89x+39.95$

b. If the truck is driven 110 miles, then its rent will be $\$137.85$.

If the truck is driven 230 miles, then its rent will be $\$244.65$.

Explanation of Solution

Given:

The truck rental company rents the truck for one day by charging $\$39.95$ plus $\$0.89$ per mile.

Formula Used:

A linear equation is of the form $f(x)=mx+c$, where $m$ is the average rate if change of that function and $c$ is the $y\text{-intercept}$, which is the initial value of the function when $x=0$.

Calculation:

Here, we can see that $\$39.95$ is the initial rent of the truck irrespective of the miles driven.

Let the number of miles travelled be $x$.

Therefore, for each $x$, $\$0.89$ is added to the rent.

a.

Thus, the rental cost of the truck will be

$C(x)=0.89x+39.95$

b.

When $x=110$, the rent of the truck will be

$C(110)=0.89(110)+39.95$

$=137.85$

Therefore, if the truck is driven 110 miles, then its rent will be $\$137.85$.

When $x=230$, the rent of the truck will be

$C(230)=0.89(230)+39.95$

$=244.65$

Therefore, if the truck is driven 230 miles, then its rent will be $\$244.65$.