Algebra 1 help please?

Question

To become a member of an ice skating rink, you have to pay a $30 membership fee. The cost of admission to the rink is $5 for members and $7 for non-members. After how many visits to the rink is the total cost for members, including the membership fee, the same as the total cost for nonmembers?

I already know that the answer is 15 visits, but the question wants me to show a plan or equation then solve and show my work. What is the proper Algabraic equation to solve this problem? I am in Algebra 1.

Thank you in advance, I really appreciate the help!

Answer 1

Set up 2 equations that represent the cost as a function of the number of visits  

 

For members:         f(x) = 5*x + 30  

 

For non-members:  g(x) = 7*x  

 

To find where the 2 costs are the same set f(x) = g(x) and solve for x