Question

The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 42 minutes of calls is $23.70, and the remaining credit after 53 minutes of calls is $22.05 . What is the remaining credit after 61 minutes of calls?

Answer 1

The remaining credit after 61 minutes of calls is $20.85.

Explanation:

The credit remaining after t minutes can be modeled by a linear function is the following format:

`C(t) = C(0) - at`

In which C(0) is the initial amount of credit and a is the cost of a minute.

The remaining credit after 42 minutes of calls is $23.70

This means that
`C(42) = 23.70`

So

`C(t) = C(0) - at`

`23.70 = C(0) - 42a`

`C(0) = 42a + 23.70`

The remaining credit after 53 minutes of calls is $22.05.

This means that
`C(53) = 22.05`

So

`C(t) = C(0) - at`

`22.05 = C(0) - 53a`

`C(0) = 22.05 + 53a`

From above:

`C(0) = 42a + 23.70`

So

`42a + 23.70 = 22.05 + 53a`

`11a = 1.65`

`a = (1.65)/(11)`

`a = 0.15`

`C(0) = 42*0.15 + 23.70 = 30`

So

`C(t) = C(0) - at`

`C(t) = 30 - 0.15t`

What is the remaining credit after 61 minutes of calls?

This is C(61).

`C(t) = 30 - 0.15*61 = 20.85`

The remaining credit after 61 minutes of calls is $20.85.