Question

students and adults purchased tickets for a recent basketball playoff game. Student tickets cost $5 each and adult tickets cost $10. A total of $4500 was collected 700 tickets were sold. how much more money would have been collected at the playoff game if the ticket booth charged $15 for student and adult tickets

Answer 1

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.