Members at a swim club pay $5 lesson plus a one-time fee of $60. nonmembers pay $11 per lesson. how many lessons would both a member and a nonmember have to take to pay the same amount?

10 lessons
you can do it by creating a chart or algebraically

like below
for the members we have 
60 (flat fee) + 5 * x (where x represents the number of lessons)
for nonmembers is simple lessons= 11 * x (x represents the number of lessons)
we will set both of these equations equal
60 + 5 * x = 11 * x  , we will simplify and get 5x+60=11x
60= 11x-5x , so 60= 6x , x=10 
after 10 lessons
x