Chapter 9.1, Problem 27IP

(a)

To determine

To identify: The dependent and the independent variables. Also, write a function to represent the total cost of any number of miles driven.

Answer to Problem 27IP

A function to represent the total cost of any number of miles driven is as follows:

  $c(x)=50+0.55x$

Explanation of Solution

Given information:

Money spent by Logan to rent the truck = $\$128.10$

Charge of the truck = $\$50$

Charge of driving the truck per mile = $\$0.55$

Calculation:

Let total cost be c.

Let total number of miles bex.

Since the total cost depends upon the number of miles driven, the total cost c is the dependent variable and the number of miles drivenx is the independent variable.

Charge of driving the truck per mile = $\$0.55$ Therefore, charge of driving the truck for x miles = $\$0.55x$

A function to represent the total cost of any number of miles driven can be evaluated as follows:

Words $\text{Total cost = Charge of truck + Cost on number of miles driven}$

Function $c(x)=50+0.55x$

(b)

To determine

To calculate: Number of miles the truck is driven for using the equation found in part (a).

Answer to Problem 27IP

The truck is driven for $\text{142 miles}$ .

Explanation of Solution

Given information:

Money spent by Logan to rent the truck = $\$128.10$

Charge of the truck = $\$50$

Charge of driving the truck per mile = $\$0.55$

Calculation: The number of miles the truck is driven for is calculated as follows:

  $\begin{array}{l}c(x)=50+0.55x[\text{Write the function]}\\ \text{128}\text{.10}=50+0.55x[\text{Substitute 128}\text{.10 for }c(x)]\\ \text{0}\text{.55}x=78.1[\text{Subtract 50 from both sides]}\\ x=142[\text{Divide both sides by 0}\text{.55]}\end{array}$