# The range of minutes for which plan B be financially advantageous.

### 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 108E
To determine

## To evaluate: The range of minutes for which plan B be financially advantageous.

Expert Solution

Plan B will be financially advantageous if the minutes are less than 285.71min_.

### Explanation of Solution

Given:

The offers from phone service provider is given as,

Plan A: $25 per month and 5ȼ per minute. Plan B:$5 per month and 12ȼ per minute.

Calculation:

Identify the variables:

It is required to find the range of minutes for which plan B be financially advantageous. Let the number of minutes be x.

Translate from words to algebra:

Number of minutes is x.

Cost for Plan A is 25+0.05x.

Cost for Plan B is 5+0.12x.

Set up the model:

Plan B will be financially advantageous if cost of plan B is less than that of plan A. That is,

Cost for Plan B< Cost of Plan A5+0.12x<25+0.05x

Solve 5+0.12x<25+0.05x as follows:

5+0.12x<25+0.05x5+0.12x5<25+0.05x50.12x<20+0.05x

Further solve the above equation as follows:

0.07x<20x<285.71

Therefore, plan B will be financially advantageous if the minutes are less than 285.71min_.

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