How many times would a member and a non member have to rent a boat in order to pay the same amount

X = number of times they rent a boat. 

Members 
Cost = 105 + 9.50x
Non-members because members don't have to pay the 105 so we gotta leave it out. 
Cost = 14.75x 

Now to determine whether the cost would be equal, we need to set the two equations equal to each other.

105 + 9.50x = 14.75x 

Now solve for x

105 = 5.25x
 
20 = x 

That's your answer. They would have to rent 20 times to equal each other.