The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $9. The auditorium can hold no more than 80 people. The drama club must make no less than $530 from ticket sales to cover the show's costs. If 31 student tickets were sold, determine the minimum number of adult tickets that the drama club must sell in order to meet the show's expenses.
Let x be the number of adult tickets sold.
Therefore, the total revenue from student tickets is 31 student tickets x $4 = $124.
The total revenue from adult tickets is x adult tickets x $9 = $9x.
The total revenue from ticket sales must be at least $530, so we can write the following equation:
$124 + $9x ≥ $530
$9x ≥ $530 - $124
$9x ≥ $406
x ≥ $406 / $9
x ≥ 45.11
Since we can only sell whole numbers of tickets, the drama club must sell at least 46 adult tickets in order to meet the show's expenses.