Question

One long-distance phone plan costs $\$ 3.95$ per month plus $\$ 0.08$ per minute of use. A second long-distance plan costs $\$ 0.10$ per minute for the first 50 minutes used each month and then $\$ 0.15$ per minute after that. Which plan is cheaper if you use an average of 75 long-distance minutes per month?

Name: Problem 34, Chapter 4: Geometry
Uploaded: 2020-05-01T16:29:08-08:00
Duration: 3 min 15 s
Channel: Dawn Getman
Description: One long-distance phone plan costs 3.95 per month plus 0.08 per minute of use. A second long-distance plan costs 0.10 per minute for the first 50 minutes used each month and then 0.15 per minute after that. Which plan is cheaper if you use an average of 75 long-distance minutes per month?

   One long-distance phone plan costs $\$ 3.95$ per month plus $\$ 0.08$ per minute of use. A second long-distance plan costs $\$ 0.10$ per minute for the first 50 minutes used each month and then $\$ 0.15$ per minute after that. Which plan is cheaper if you use an average of 75 long-distance minutes per month?

Geometry

Edward Burger, David… 1st Edition

Chapter 4, Problem 34

Instant Answer

Solved by Expert Dawn Getman

05/01/2020

Step 1

The first plan costs a flat fee of \$3.95 per month plus \$0.08 per minute of use. So, if we use 75 minutes per month, the total cost of the first plan would be: \[ \$3.95 + \$0.08 \times 75 = \$3.95 + \$6 = \$9.95 \] Show more…

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One long-distance phone plan costs $\$ 3.95$ per month plus $\$ 0.08$ per minute of use. A second long-distance plan costs $\$ 0.10$ per minute for the first 50 minutes used each month and then $\$ 0.15$ per minute after that. Which plan is cheaper if you use an average of 75 long-distance minutes per month?

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Key Concepts

Linear Functions

Linear functions describe relationships where a change in one quantity produces a proportional change in another. In the context of cost models, a linear function allows calculation of total cost by adding a fixed fee to a variable cost that is directly proportional to usage.

Piecewise Functions

Piecewise functions are used to model situations where the rule for calculating outcomes, such as cost, changes based on the value of an independent variable. They enable different formulas or rates to be applied depending on the range or interval in which the usage falls.

Cost Comparison

Cost comparison involves evaluating and contrasting different cost models to determine which one is more economical under given usage conditions. This process typically involves calculating the total cost for each model using the relevant functions and then comparing the results.

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