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 surcharge. Write a linear function that models this situation.
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To write a linear function that models this situation, we need to determine the total cost as a function of the number of students attending.
Let's start by breaking down the costs:
1. There is a one-time handling fee of $3, which is constant regardless of the number of students attending.
2. Each student ticket costs $25.
3. Additionally, there is a $2 surcharge per ticket for all the students.
Based on this information, we can write the linear function as follows:
Cost = (Number of Students) * (Ticket Cost per Student) + Handling Fee + Surcharge
The ticket cost per student is $25, which can be expressed as 25 * (Number of Students). Similarly, the surcharge is $2 per student, so we can write it as 2 * (Number of Students).
Now, let's incorporate these values into our linear function:
Cost = (Number of Students) * (25) + 3 + (Number of Students) * (2)
Simplifying this expression, we get:
Cost = 25 * (Number of Students) + 3 + 2 * (Number of Students)
Combining like terms, we find the final linear function that models this situation is:
Cost = 27 * (Number of Students) + 3
Thus, the linear function is Cost = 27x + 3, where x represents the number of students attending.