The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6.50 and each adult ticket sells for $11.50. The auditorium can hold a maximum of 120 people. The drama club must make no less than $1100 from ticket sales to cover the show's costs. If 70 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.
Let x be the number of student tickets that the drama club must sell.
The total revenue from adult tickets is 70 * $11.50 = $805.
The total revenue from student tickets is x * $6.50 = $6.50x.
The total revenue from all ticket sales must be at least $1100, so:
$805 + $6.50x ≥ $1100
$6.50x ≥ $295
x ≥ 45.38
Since we cannot sell a fraction of a ticket, the drama club must sell a minimum of 46 student tickets to meet the show's expenses.