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

12x50=600 so 60 left
15x50=750 so 60 left
so the administration fee is 60

Answer 2

Answer:

a=$50 One time administration fee

Step-by-step explanation:

This is a function. Let's model it. Knowing that the Cost of Parking permit is made up of One time administration fee for all, and a monthly payment for everyone.  What's changing here is the amount of Parking Time. So Let's model and solve this Linear System.

C(t)= Cost of Parking Permit. (t= time is given in months)

a= One time administration fee

b = monthly payment

First Case: A permit purchased for 12 months costs $660.

660=12a +b

Second case: A permit purchased for 15 months costs $810

810=15a+b

                                 

660=12a+b    * -5         Addition Method

810=15a+b  * 4

-3300=-60a-5b

 3240= 60a+4b

--------------------------

-60=-b

b=60 monthly fee

                                        Plug in the first equation to find out a.

660 =12a +60

660-60=12a

600=12a

a=$50 One time administration fee

Testing it

$660= 12(50)+60 as 810=15(50)+60 .