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?

Question

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.