# The range of miles for Plan B to save money. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.7, Problem 107E
To determine

## To evaluate: The range of miles for Plan B to save money.

Expert Solution

The range is more than 200 miles.

### Explanation of Solution

Given:

The offers for car rent are as follows:

Plan A: $30 per day and 10 ȼ per mile. Plan B:$50 per day with free unlimited mileage.

Calculation:

Identify the variables:

It is required to find the range of miles for Plan B to save money. Let the number of miles be x.

Translate from words to algebra:

The number of miles be x.

Daily cost for plan A will be 30+0.10x.

Daily cost for plan B will be 50.

Set up the model:

Plan B should cost less than plan A for Plan B to save money. That is,

Cost for Plan B< Cost of Plan A50<30+0.10x

Solve 50<30+0.10x as follows:

50<30+0.10x20<0.10x                            [Subtract 30 on both sides]20(10)<0.10x(10)              [Multiply by 10]200<xx>200

Thus, the range of miles for Plan B to save money will be when x>200. That is, when the range of miles is more than 200 miles.

Therefore, the range is more than 200 miles.

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