Sheilas cell phone plan consists of a monthly rate and a fee for each minute she talks over 500 minutes per month. her july bill showed 630 minutes and a total charge of $53.55. her august bill showed 709 minutes of use and a total charge of $63.03. what is the monthly rate and how much is she being charged for her extra minutes?

First of all we need to formulate two equations.

x = monthly fee per minute
y = monthly fee per minute over 500

500x + 130y = $53.55
500x + 209y = $63.03

Since we know that 500x = $53.55 - 130y we can substitute.

($53.55 - 130y) + 209y = $63.03
79y = 9.48
y = $0.12

Now we can substitute y into the other equation.

500x = $53.55 - 130(0.12)
500x = $53.55 - $15.6
500x = $37.95

So the answer is $37.95 monthly for 500 minutes with an over quota fee of $0.12 per minute.