Question

The drama club is selling tickets to their 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. The drama club must make 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.

Answer 1

The drama club needs to sell at least 52 student tickets at $7.50 each, in addition to the 55 adult tickets sold at $9.50, to meet their goal of making at least $910 to cover the show's costs.

Step-by-step explanation:

The drama club is selling tickets to their play, with student tickets priced at $7.50 and adult tickets at $9.50, to cover the show's expenses which must be at least $910. Their auditorium can hold a maximum of 108 people, and they have sold 55 adult tickets. To find the minimum number of student tickets they need to sell, we set up the following inequality based on their pricing:

$9.50 × 55 (adult tickets) + $7.50 × x (student tickets) ≥ $910
Substituting the adult ticket sales into the inequality gives us:

$9.50 × 55 + $7.50 × x ≥ $910

$522.50 + $7.50 × x ≥ $910

$7.50 × x ≥ $910 - $522.50

x ≥ ($910 - $522.50) / $7.50

x ≥ $387.50 / $7.50

x ≥ 51.67

Since you can't sell a fraction of a ticket, the drama club must sell at least 52 student tickets to meet the minimum revenue required for their expenses.