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 $9. The auditorium can hold a maximum of 120 people. The drama club must make a minimum of $920 from ticket sales to cover the show's costs. If 63 adult tickets were sold, determine all possible values for the 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 sold.
Total revenue from student tickets = 6.50x
Total revenue from adult tickets = 9(63) = 567
Total revenue from all tickets = 6.50x + 567
Since the drama club must make at least $920, we have:
6.50x + 567 ≥ 920
6.50x ≥ 353
x ≥ 54.31
Since x must be a whole number, the drama club must sell at least 55 student tickets to meet the show's expenses.