Question

The drama club sold 1500 tickets for the end-of-year performance. Admission prices were $12 for adults and $6 for students. The total amount collected at the box office was $15,600. How many students attended the play?

Answer 1

After setting up and solving a system of equations based on the total number of tickets sold and the total amount collected from sales, it was determined that 400 students attended the play.

Step-by-step explanation:

To determine how many students attended the play, we need to set up a system of equations based on the information provided about ticket sales and admissions prices:

• Let x be the number of adult tickets sold, each costing $12.
• Let y be the number of student tickets sold, each costing $6.

We are given the following two pieces of information to form our equations:

1. The total number of tickets sold was 1500, so x + y = 1500.
2. The total amount collected was $15,600, so 12x + 6y = $15,600.

Solving this system of equations, we can find the values of x and y. Dividing the second equation by 6 simplifies it to 2x + y = 2600. By subtracting the first equation from this new equation, we get x = 2600 - 1500, which means x = 1100. Therefore, there were 1100 adult tickets sold. To find the number of student tickets, substitute the value of x into the first equation: 1100 + y = 1500, which gives us y = 1500 - 1100, so y = 400. Thus, there were 400 students who attended the play.