5. The Valley High School student council is planning a dance. The school has 135 students. The lowest possible ticket price is $\$ 1.00$, and they estimate that for every $\$ 0.50$ increase in ticket price, 15 fewer students will attend. What ticket price will maximize the student council's profit?
$\$ 3.15$
$\$ 2.65$
$\$ 2.50$
$\$ 2.75$

Step 1 ：The Valley High School student council is planning a dance. The school has 135 students. The lowest possible ticket price is $1.00, and they estimate that for every $0.50 increase in ticket price, 15 fewer students will attend. What ticket price will maximize the student council's profit?

Step 2 ：The profit is calculated by multiplying the ticket price by the number of students attending. The number of students attending is a function of the ticket price.

Step 3 ：We can create a function to calculate the profit for each possible ticket price and then find the maximum profit.

Step 4 ：Let's consider the following ticket prices: $1.00, $1.50, $2.00, $2.50, $3.00, $3.50, $4.00, $4.50, $5.00, $5.50.

Step 5 ：The corresponding profits for these ticket prices are: $135.00, $180.00, $210.00, $225.00, $225.00, $210.00, $180.00, $135.00, $75.00, $0.00.

Step 6 ：The maximum profit is obtained for the ticket price of $2.50.

Step 7 ：Final Answer: The ticket price that will maximize the student council's profit is \(\boxed{\$2.50}\).