Question

15. A total of 2000 people attended a benefit concert was held to raise money for a children foundation. Student ticket cost $2 and an adult ticket cost $3. If the organizer raises a total of $5050, how many students attended the concert?
Let : x = number of students
2000 - x = number of adults

Answer 1

Let's denote the number of student tickets as \( x \) and the number of adult tickets as \( 2000 - x \).

From the problem, we know:

1. The total number of attendees is 2000:
\[
x + (2000 - x) = 2000
\]
This confirms our setup.

2. The total amount raised is $5050, which can be expressed with the ticket prices:

- Student ticket price = $2
- Adult ticket price = $3

Therefore, the equation for total revenue is:
\[
2x + 3(2000 - x) = 5050
\]

Now, let's simplify this equation:

\[
2x + 6000 - 3x = 5050
\]

Combine like terms:

\[
-1x + 6000 = 5050
\]

Subtract 6000 from both sides:

\[
-x = 5050 - 6000
\]
\[
-x = -950
\]

Multiply both sides by -1:

\[
x = 950
\]

So, the number of students who attended the concert is \( \boxed{950} \).

To verify, let's find the number of adults:

\[
2000 - 950 = 1050
\]

Now, we check the total revenue:

\[
2(950) + 3(1050) = 1900 + 3150 = 5050
\]

This confirms that our solution is correct, and 950 students attended the concert.