Question

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 $8.50. The auditorium can hold at most 110 people. The drama club must make no less than $680 from ticket sales to cover the show's costs. Also, they can sell no more than 70 adult tickets. If xx represents the number of student tickets sold and yy represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

74 or 73

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.