The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $5.50 and each adult ticket sells for $7.50. The auditorium can hold a maximum of 140 people. The drama club must make at least $910 from ticket sales to cover the show's costs. If 66 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. If there are no possible solutions, submit an empty answer.

Step-by-step explanation:

We are going to assume that the show is sold out. If 66 student tickets were sold, we only have 74 adult tickets to sell. Based on that information, we then have to use an inequality to find out if the number of adult tickets we have to sell to meet our money requirements is more than the amount of seating we have left after 66 seats were taken by students. Our inequality looks like this:

5.50 (66) + 7.50 (a) ≥ 910 and

363 + 7.50a ≥ 910 and

7.50a ≥ 547 so

a ≥ 73

In order to meet our money requirement, we have to sell 73 adult tickets. Since we have 74 seats left, we are good.

Answer: {73,74}