Question

Each student ticket sells for $5 and each adult ticket sells for $7.50. The auditorium can hold at most 125 people. The drama club must make no less than $790 from ticket sales to cover the show's costs. If 73 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. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.

Answer 1

(49 ≤ x x ≤ 52)

Explanation:

Let x represent the number of student tickets that must be sold.

The auditorium can hold at most 125 people. If 73 adult tickets were sold, it means that

73 + x ≤ 125

x ≤ 125 - 73

x ≤ 52

Each student ticket sells for $5 and each adult ticket sells for $7.50.

The drama club must make no less than $790 from ticket sales to cover the show's costs. This means that

5x + 7.5 × 73 ≥ 790

5x + 7.5 × 73 ≥ 790

5x +547.5 ≥ 790

5x ≥ 790 - 547.5

5x ≥ 242.5

x ≥ 242.5/5

x ≥ 48.5

Therefore, the number of tickets that must be sold must not be below 49 and must not be above 52. This is expressed as

(49 ≤ x x ≤ 52)