Question

A basic cellular phone plan costs $4 per month for 70 calling minutes. Additional time costs $0.10 per minute. The formula C= 4+0.10(x-70) gives the monthly cost for this plan, C, for x calling minutes, where x>70. How many calling minutes are possible for a monthly cost of at least $7 and at most $8?

Answer 1

Answer:

For a monthly cost of at least $7 and at most $8, you can have between 100 and 110 calling minutes.

Step-by-step explanation:

The problem states that the monthly cost of a celular plan is modeled by the following function:

$C(x) = 4 + 0.10(x-70)$

In which C(x) is the monthly cost and x is the number of calling minutes.

How many calling minutes are needed for a monthly cost of at least $7?

This can be solved by the following inequality:

$C(x) \geq 7$

$4 + 0.10(x - 70) \geq 7$

$4 + 0.10x - 7 \geq 7$

$0.10x \geq 10$

$x \geq \frac{10}{0.1}$

$x \geq 100$

For a monthly cost of at least $7, you need to have at least 100 calling minutes.

How many calling minutes are needed for a monthly cost of at most 8:

$C(x) \leq 8$

$4 + 0.10(x - 70) \leq 8$

$4 + 0.10x - 7 \leq 8$

$0.10x \leq 11$

$x \leq \frac{11}{0.1}$

$x \leq 110$

For a monthly cost of at most $8, you need to have at most 110 calling minutes.

For a monthly cost of at least $7 and at most $8, you can have between 100 and 110 calling minutes.