The drama club plans to attend a professional production. From 10 to 35 students will go. There is a one-time handling fee of $3. each ticket costs $25 plus $2 surcharges. Write a linear function that models this situation. (show your work)

The drama club plans to attend a professional production. From 10 to 35 students will go. There is a one-time handling fee of $3. each ticket costs $25 plus $2 surcharges. Write a linear function that models this situation. (show your work)

To write a linear function that models this situation, we need to determine the total cost based on the number of students attending the professional production.

Let's break down the cost:
- There is a one-time handling fee of $3 for the entire group.
- Each ticket costs $25.
- There is a $2 surcharge per ticket.

Let's define our variables:
- Let's use "x" to represent the number of students attending the professional production.

Now, let's calculate the total cost:
- The handling fee is a one-time fee of $3, so we add $3 to the total cost.
- Each student needs a ticket, which costs $25. So, we multiply the number of students (x) by $25 to get the ticket cost.
- There is a $2 surcharge on each ticket, so we multiply the number of students (x) by $2 to get the surcharge cost.

The total cost, C(x), can be calculated using the following linear equation:
C(x) = handling fee + (ticket cost + surcharge cost)

C(x) = 3 + (25x + 2x)

Combining like terms, we have:
C(x) = 3 + 27x

Therefore, the linear function that models this situation is C(x) = 27x + 3.