A movie theater offers two options for membership. The first option costs $10 per ticket by it an initial fee of $20. The second option costs $7.50 per ticket but an initial fee of $40. After how many tickets are both options the same price?
Let the number of tickets be represented by x.
For the first option, the total cost will be 10x + 20.
For the second option, the total cost will be 7.5x + 40.
Setting these two expressions equal to each other, we have:
10x + 20 = 7.5x + 40
2.5x = 20
x = 8
Therefore, after purchasing 8 tickets, both options will be the same price.