A movie theater offers two options for membership. The first option costs $7.50 per ticket but an initial fee of $10. The second option costs $5 per ticket but an initial fee of $55 After how many tickets are both options the same price?
____ tickets
Let x be the number of tickets.
The cost of option 1 is 7.50x + 10.
The cost of option 2 is 5x + 55.
Setting the two costs equal to each other, we have 7.50x + 10 = 5x + 55.
Subtracting 5x from both sides, we get 2.50x + 10 = 55.
Subtracting 10 from both sides, we get 2.50x = 45.
Dividing both sides by 2.50, we get x = 18.
After 18 tickets, both options will cost the same. Answer: \boxed{18}.