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 costs810. What is the administration fee?

1) $505
2) $560

Answer 1

The administration fee for the parking permit is $60.

Step-by-step explanation:

Let's assume the one-time administration fee is 'A' and the monthly fee is 'M'.

From the given information, we know that a parking permit purchased for 12 months costs $660 and a permit purchased for 15 months costs $810. Using this information, we can set up two equations:

12M + A = 660

15M + A = 810

Subtracting the first equation from the second equation, we get:

3M = 150

Dividing both sides of the equation by 3, we find:

M = 50

Substituting this value of M back into one of the original equations, we can solve for A:

12(50) + A = 660

600 + A = 660

A = 60

Therefore, the administration fee is $60. So the correct answer is option 1) $505.