Final answer:
To find the number of adult tickets sold, set up an equation based on the total revenue from all ticket sales. Solve the equation to find the value of x, which represents the number of adult tickets sold. The answer is 30 adult tickets sold.
Step-by-step explanation:
To find the number of adult tickets sold, let's assign variables to represent the number of adult tickets and student tickets. Let's say the number of adult tickets is x. According to the problem, the number of student tickets sold is 30 more than the number of adult tickets, so the number of student tickets would be x + 30.
Given that each adult ticket sells for $9 and each student ticket sells for $4.50, we can set up an equation based on the total revenue from all ticket sales. The equation is:
9x + 4.50(x + 30) = 540
Now, we can solve this equation to find the value of x, which represents the number of adult tickets sold.
Combining like terms, we have:
9x + 4.50x + 135 = 540
Combining the x terms, we get:
13.50x + 135 = 540
Subtracting 135 from both sides of the equation, we have:
13.50x = 405
Finally, dividing both sides of the equation by 13.50, we find that x = 30.
Therefore, 30 adult tickets were sold.