Question

The drama club is selling tickets for the play to raise money for the show's expenses. Each student ticket sells for $7.50, and each adult ticket sells for $9.50. The auditorium can hold at most 108 people, and the drama club must take no less than $910 from ticket sales to cover the show's costs. If 55 adult tickets were sold, determine the minimum number of student tickets that the drama club must sell in order to meet the show's expenses.

a) 30 student tickets
b) 35 student tickets
c) 40 student tickets
d) 45 student tickets

Answer 1

The minimum number of student tickets that the drama club must sell to meet the show's expenses is 191 student tickets.

Step-by-step explanation:

To determine the minimum number of student tickets that the drama club must sell in order to meet the show's expenses, we need to calculate the total revenue from ticket sales and then subtract the revenue from adult tickets. The revenue from student tickets can be found by multiplying the number of student tickets by the price per student ticket. Since the drama club must take no less than $910 from ticket sales, we can set up the following equation:

Revenue from student tickets - Revenue from adult tickets = $910

Let's calculate:

Revenue from student tickets:

1. Price per student ticket: $7.50
2. Number of student tickets: Let's assume there are x student tickets sold

So, the equation becomes:

7.50x - (55 imes 9.50) = 910

Simplifying the equation:

7.50x - 522.50 = 910

7.50x = 1432.50

x = 1432.50/7.50

x ≈ 190.87

Since we can't sell a fraction of a ticket, the minimum number of student tickets that the drama club must sell is 191 student tickets.