Chapter 3, Problem 10CST

a.

To determine

TO-DETERMINE how many miles $m$ one should have to drive before the cost of renting a van for one day from company A would be less than the cost of renting a van for one day from company B.

Answer to Problem 10CST

  $214.28\text{ miles}$

Explanation of Solution

Given:

The daily charge and charge per mile of both the companies are given in the above table.

  

Calculation:

Let the miles travelled by Company A be $m$

  $\begin{array}{l}0.35m<75\\ 0.35m÷0.35<75÷0.35\left[\text{dividing both sides by 0}\text{.35}\right]\\ m<214.28\end{array}$

Hence, the van from company A will have to be driven $214.28$ miles before the cost of renting a van for one day from company A is less than the cost of renting a van for one day from company B.

b.

To determine

To graph the inequality from part a

Explanation of Solution

Given information:

The van from company A will have to be driven $214.28$ miles before the cost of renting a van for one day from company A is less than the cost of renting a van for one day from company B.

  $m<214.28$

Graph:

  

c.

To determine

TO-DETERMINE the less expensive company if 100 miles per day is driven

Answer to Problem 10CST

Company A

Explanation of Solution

Given information:

The daily charge and charge per mile of both the companies are given in the above table.

  

Calculation:

The result can be obtained by

Cost of driving $100$ miles per day from company A = $100\text{ miles}\times \$.35=\$35\left[\text{multiply}\right]$

Cost of driving $100$ miles per day from company B = $100\text{ miles}\times \$.39=\$39\left[\text{multiply}\right]$

The cost per mile of company A is less than the cost per mile of company B.

Hence, Company A is less expensive if $100$ miles is driven per day.