Question

A holiday musical performance is attended by 482 people. Adult tickets cost $12 and children's tickets cost $6. The total revenue collected from ticket sales was $5,250. How many adults attended the concert?

A) 250 adults
B) 300 adults
C) 325 adults
D) 350 adults

Answer 1

Using a system of linear equations, it was determined that the number of adult tickets sold is 393, but this is not an option provided in the multiple-choice question, which may indicate errors in the question or answer options.

Step-by-step explanation:

The student is tasked with solving a problem that involves determining the number of adults who attended a concert based on the total number of attendees and the revenue collected from ticket sales, where adult tickets and children's tickets have different prices. This problem can be solved using a system of linear equations.

Let A be the number of adult tickets sold, and C be the number of children's tickets sold. We are given the following equations:

1. 
   
3. A + C = 482 (total number of tickets sold)
4. 
   
6. 12A + 6C = 5250 (total revenue from ticket sales)

By multiplying the first equation by 6, we get:

1. 
   
3. 6A + 6C = 2892
4. 
   
6. 12A + 6C = 5250

Subtracting the first new equation from the second:

1. 
   
3. 12A + 6C - (6A + 6C) = 5250 - 2892
4. 
   
6. 6A = 2358

Dividing both sides by 6, we find A = 393. So, the number of adult tickets sold is 393.

However, this answer is not in the multiple-choice options provided, indicating potential calculation or transcription errors in the question or options given.