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.

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.

mertsj · Answer

cost = membership + fee(sessons)

mertsj · Answer

Substitute into that twice and you will have your system of equations.

anonymous · Answer

you can just about do this in your head. 
5 more sessions cost 15 more dollars, so price per session is 
$$\frac{15}{5}=3$$ (this is the slope of line in algebra)

then since we know each session cost $3, and we know if you take ten sessions you pay $40, that means $30 for all the sessions leaving $10 for the membership fee