Question

The telephone company offers two billing plans for local calls. Plan 1 charges ​$22 per month for unlimited calls and Plan 2 charges ​$19 per month plus ​$0.05 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.

Answer 1

A.
`22<19+0.05x`

B. If a customer makes more than 60 monthly calls, then Plan 1 is more economical

Explanation:

Let x be the number of calls, y - total cost per month

Plan 1: $22 per month for unlimited calls, then

`y=22`

Plan 2: ​$19 per month plus ​$0.05 per call ($0.05x for x calls). Then

`y=19+0.05x`

A. If Plan 1 is more economical than Plan 2, then the total cost in Plan 1 is less than the total cost in Plan 2. Thus,

`22<19+0.05x`

B. Solve this inequality:

`22<19+0.05x\\ \\0.05x+19>22\\ \\0.05x+19-19>22-19\\ \\0.05x>3\\ \\5x>300\ [\text{ Multiplied by 100}]\\ \\x>60\ [\text{ Divided by 5}]`

Meaning: If a customer makes more than 60 monthly calls, then Plan 1 is more economical