the cost of a parking permit consists of a one - time administration fee plus a monthly fee. a permit…

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? $50 $54 $55 $60

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? $50 $54 $55 $60

Answer

Explanation:

Step1: Find the cost of 3 - month difference

The difference in months is $15 - 12=3$ months, and the difference in cost is $810 - 660 = 150$ dollars. So the monthly fee $m$ is $\frac{810 - 660}{15 - 12}$. $m=\frac{150}{3}=50$ dollars per month.

Step2: Find the administration fee

Let the administration fee be $a$. For a 12 - month permit, the cost equation is $a + 12m=660$. Substitute $m = 50$ into the equation: $a+12\times50 = 660$. Then $a+600 = 660$. Solve for $a$: $a=660 - 600$. $a = 60$ dollars.

Answer:

$60$