Question

The cost of a parking permit consists of a one-time administration fee plus a monthly fee. a permit purchased for 12 months costs $660. a permit purchased for 15 months costs $810. what is the administration fee?

Answer 1

The general equation that may be used to determine the total cost of the parking permit,
P = A + mt
where P is the total cost, A is the administration fee, m is the monthly fee and t is the number of months. Substituting the known values to the equation,
(1) 660 = A + 12m
(2) 810 = A + 15 m

Solving for the solutions of the equation gives A = 60 and m = 50. Thus, the administration fee is $60.

Answer 2

let

x--------> the monthly fee

y--------> the administration fee

we know that

`660=y+12x` --------> equation
`1`

`810=y+15x` --------> equation
`2`

Multiply by
`-1` equation
`1`

`-660=-y-12x` ------> equation
`3`

Adds equation
`2` and equation
`3`

`810=y+15x\\-660=-y-12x\\---------\\ 810-660=15x-12x\\ 3x=150\\ x=50\ dollars`

Find the value of y

`660=y+12x\\ 660=y+12*50\\ y=660-600\\ y=60\ dollars`

therefore

the answer is

the administration fee is equal to
`60\ dollars`