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 $9. The auditorium can hold no more than 90 people. The drama club must make a minimum of $610 from ticket sales to cover the show's costs. If 57 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.

Answer 1

The drama club must sell a minimum of 37 adult tickets in order to meet the show's expenses.

Step-by-step explanation:

To determine the minimum number of adult tickets that the drama club must sell in order to meet the show's expenses, we need to calculate the remaining amount that needs to be raised after selling the student tickets.

The drama club must make a minimum of $610 from ticket sales. Since 57 student tickets were sold at $5 each, the total revenue from student tickets is 57 * $5 = $285.

Therefore, the remaining amount that needs to be raised is $610 - $285 = $325.

Since each adult ticket sells for $9, we can calculate the minimum number of adult tickets that need to be sold by dividing the remaining amount by the price of an adult ticket:

$325 / $9 = 36.11 (rounded up to 37).

Therefore, the drama club must sell a minimum of 37 adult tickets in order to meet the show's expenses.

Answer 2

NO SOLUTION

Step-by-step explanation:

The maximum number of adult tickets that can be sold is ...

90 -57 = 33

The revenue from sale of 57 student and 33 adult tickets is ...

57×$5 + 33×$9 = $285 +297 = $582

The drama club cannot meet expenses by selling available seats.