System of Inequalities Word Problems

Question

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $5 and each adult ticket sells for $8. The auditorium can hold a maximum of 122 people. The drama club must make no less than $790 from ticket sales to cover the show's costs. If 69 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.

Answer 1

There is no solution because if you have 69 students sold then 69 * $5 = 345. After subtracting that from the minimum you need to make 790-345 = 445. to make at least $445 with $8 per adult you would need a minimum of 56 adults 445/8 is 55.625 and when you add 56 plus 69 students you are above the maximum capacity 69+56 = 125 and 125 > 122. so it would be an empty answer.

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