Question

A basic cellular package costs $30/month for 60 minutes of calling with an additional charge of $0.40/minute beyond that time. The cost function C (2) for using x minutes would be • If you used 60 minutes or less, i.e. if if x < 60, then C (x) = 30 (the base charge). If you used more than 60 minutes, i.e. (x – 60 minutes more than the plan came with, you would pay an additional $0.40 for each of those (x – 60 minutes. Your total bill would be C (x) = 30 + 0.40 (x – 60). If you want to keep your bill at $50 or lower for the month, what is the maximum number of calling minutes you can use? minutes. The maximum calling minutes you can use is ? Number​

Answer 1

The maximum number of minutes to keep the cost at $50 or less is 110 minutes

Explanation:

Given

`C(x) = 30` ----
`x < 60`

`C(x) = 30 + 0.40(x - 60)` ---
`x \ge 60`

Required

`C(x) = 50` ---- find x

We have:

`C(x) = 30 + 0.40(x - 60)`

Substitute 50 for C(x)

`50 = 30 + 0.40(x - 60)`

Subtract 30 from both sides

`20 = 0.40(x - 60)`

Divide both sides by 0.40

`50 = x - 60`

Add 60 to both sides

`110 = x`

`x =110`