Final answer:
The drama club must sell a minimum of 36 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 total revenue from ticket sales. The drama club sells each student ticket for $8 and each adult ticket for $11.50. Given that 43 student tickets were already sold, we can calculate the revenue from student tickets as:
- Revenue from student tickets = Number of student tickets sold * Price per student ticket = 43 * 8 = $344
To meet the show's expenses, the drama club needs to make at least $760 from ticket sales, so the minimum revenue from adult tickets can be calculated as:
- Minimum revenue from adult tickets = Total revenue needed - Revenue from student tickets = 760 - 344 = $416
Next, we need to find out how many adult tickets need to be sold to generate a revenue of at least $416. Since each adult ticket sells for $11.50, we can calculate the minimum number of adult tickets required as:
- Minimum number of adult tickets required = Minimum revenue from adult tickets / Price per adult ticket = 416 / 11.50 ≈ 36
Therefore, the drama club must sell a minimum of 36 adult tickets in order to meet the show's expenses.