Question

To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended five sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions.
Write a system of two equations with the variables m and f in each to represent this problem.

Answer 1

m + 5f = 25....multiply by -1
m + 10f = 40
----------------
-m - 5f = -25 (result of multiplying by -1)
m + 10f = 40
-----------------add
5f = 15
f = 3

m + 10f = 40
m + 10(3) = 40
m + 30 = 40
m = 40 - 30
m = 10

so the membership fee (m) = 10 and the sessions(f) = 3