When you pay the one-time fee the cost per ticket bought can be expressed by the function below:

While the cost if you don't pay the one-time fee:

The inequality that can be used to determine the number of tickets you need to buy for the one-time fee to be less expensive is:
![\begin{gathered} c_1(x)Solving the inequality we have:[tex]\begin{gathered} 30<25x-17x \\ 30<8x \\ 8x>30 \\ x>(30)/(8) \\ x>3.75 \end{gathered}]()
For the "one-time fee" to cost less you need to buy more than 3.75 tickets.