Final answer:
To solve this problem, we set up a system of equations. We find that 300 student tickets and 150 adult tickets were sold.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's say x represents the number of student tickets sold and y represents the number of adult tickets sold.
We know that the total number of tickets sold is 450, so we can write the equation x + y = 450.
We also know that the total receipts from the ticket sales is $7,500, so we can write the equation 15x + 20y = 7500.
We now have a system of equations:
- x + y = 450
- 15x + 20y = 7500
To solve this system, we can use the method of substitution or elimination. Let's use substitution here.
From equation 1, we can isolate x by subtracting y from both sides: x = 450 - y.
Substituting this expression for x into equation 2, we get 15(450 - y) + 20y = 7500.
Simplifying the equation, we have 6750 - 15y + 20y = 7500.
Combining like terms, we get 5y = 750.
Dividing both sides by 5, we find that y = 150. Substituting this value into equation 1, we can find x: x + 150 = 450, so x = 300.
Therefore, 300 student tickets and 150 adult tickets were sold.