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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.

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When he attended 5 sessions, he paid the membership fee (m) and five times the fee for each session (5f). He paid $25.
[tex]m+5f=25[/tex]

When he attended 10 sessions, he paid the membership fee (m) and ten times the fee for each session (10f). He paid $40.
[tex]m+10f=40[/tex]

The system of equations:
[tex]m+5f=25 \ \ \ \ \ \ \ \ \ \ \ |\times (-1) \\ m+10f=40 \\ \\ -m-5f=-25 \\ \underline{m+10f=40 \ \ \ \ \ } \\ 10f-5f=40-25 \\ 5f=15 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 5 \\ f=3 \\ \\ m+5f=25 \\ m+5 \times 3=25 \\ m+15=25 \ \ \ \ \ \ \ \ \ \ \ |-15 \\ m=10[/tex]

The membership fee is $10, the fee for each session is $3.

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