Final answer:
The drama club must sell a minimum of 52 student tickets at $7.50 each, in addition to the 55 adult tickets already sold at $9.50 each, to cover the show's expenses of at least $910.
Step-by-step explanation:
To determine the minimum number of student tickets that the drama club must sell to meet the show's expenses, we need to calculate the total revenue from selling 55 adult tickets and figure out how much more money is needed to reach the target of $910.
First, we calculate the revenue from the adult tickets:
- Revenue from adult tickets = Number of adult tickets × Price per adult ticket
- Revenue from adult tickets = 55 × $9.50
- Revenue from adult tickets = $522.50
Next, we calculate the minimum amount needed from student ticket sales to cover the rest of the expenses:
- Total revenue required = $910
- Revenue needed from student tickets = Total revenue required - Revenue from adult tickets
- Revenue needed from student tickets = $910 - $522.50
- Revenue needed from student tickets = $387.50
To find the minimum number of student tickets required, we divide the revenue needed from student tickets by the price of one student ticket:
- Minimum number of student tickets = Revenue needed from student tickets ÷ Price per student ticket
- Minimum number of student tickets = $387.50 ÷ $7.50
- Minimum number of student tickets = 51.67
Since we cannot sell a fraction of a ticket, we round up to the nearest whole number, which gives us:
- Minimum number of student tickets = 52
Therefore, the minimum number of student tickets the drama club must sell is 52 to meet the expenses of at least $910.