Answer:
Let's denote:
- S = number of student tickets sold
- A = number of adult tickets sold
From the problem, we know:
1. S + A = 700 (total number of tickets sold)
2. 5S + 10A = 4500 (total amount of money collected)
Now, let's solve these equations. The most straightforward method would be substitution or elimination. Let's use substitution:
From equation 1, we can express S as 700 - A. Substitute this into equation 2:
5(700 - A) + 10A = 4500
3500 - 5A + 10A = 4500
5A = 1000
A = 200
Substitute A = 200 into equation 1 to find S:
S + 200 = 700
S = 500
So, 500 student tickets and 200 adult tickets were sold.
Now, let's calculate how much more money would have been collected if the ticket booth charged $15 for both student and adult tickets:
Total revenue = $15 * (S + A)
Total revenue = $15 * (500 + 200) = $15 * 700 = $10,500
Therefore, the amount of additional revenue would be $10,500 - $4500 = $6,000.