Question

The telephone company offers two billing plans for local calls. Plan 1 charges $21 per month for unlimited calls and Plan 2 charges $15 per month plus $0.06 per call.

a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a.
a. Let x represent the number of monthly calls.

Answer 1

Explanation:

The number of monthly calls for which Plan 1 is more economical than Plan 2 is 200 calls

If more than 200 calls are made, the plan 1 charge will be more than plan 2.

Let the number of charges per month be x

If plan 2 charges ​$16 per month plus ​$0.04 per call, this is expressed as 0.04x + 16

Price that pan 1 charges = $24

If Plan 1 is more economical than Plan 2, this is expressed as:

0.04x + 16 > 24

Subtract 16 from both sides:

0.04x + 16 - 16 > 24 - 16

0.04x > 8

x = 6/0.04

x = 200

This shows that if more than 200 calls are made, the plan 1 charge will be more than plan 2.