The drama club is selling tickets to their play to raise money for the show's expenses.

Each student ticket sells for $4.50 and each adult ticket sells for $8. The auditorium

can hold no more than 84 people. The drama club must make at least $560 from

ticket sales to cover the show's costs. If 29 student tickets were sold, determine all

possible values for the number of adult 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.

The minimum number of adult tickets required to be sold = 54

Step-by-step explanation:

Hello,

In this question, we have several variables which might confuse us here, so I'll have to break it down bit by bit.

The drama club must make a sale of $560 so as to cover cost for the event.

The seat capacity of the hall = 84

Cost of tickets for adult = $8

Cost of tickets for students = $4.50

Total number of students sold = 29

Let the number of adult ticket required = x.

(4.50 * 29) + (8 * x) = 560

130.5 + 8x = 560

8x = 560 - 130.5

8x = 429.5

Divide both sides by 8

X = 429.5 / 8

X = 53.6 approximately 54.

Minimum required number of adult tickets to be sold is 54.

(29 * 4.50) + (54 * 8) = $130.5 + $432 = $562.5