Question

The function C(x) = 29x + 54.5 represents the cost (in dollars) of cable for x months, including the $54.50 installation fee.

a. How much would you have spent on cable after 6 months?

b. How many months of cable service can you have for $344.50?

Answer 1

a.
`\$228.5`

b. 10 months.

Explanation:

a. Given the function the following function:

`C(x) = 29x + 54.5`

You can calculate the amount of money (in dollars) you would spent on cable after 6 months through this procedure:

- Substitute
`x=6` into the function:

`C(6) = 29(6) + 54.5`

- Evaluating, you get:

`C(6) =228.5`

b. The steps to calculate the number of months of cable service that you can you have for $344.50, are:

- Rewrite the function in this form:

`y = 29x + 54.5`

- Substitute
`y=344.50` into the function and then solve for "x":

`344.50= 29x + 54.5\\\\290=29x\\\\(290)/(29)=x\\\\x=10`