Question

The drama club is selling tickets to their play to raise money for the shows expenses. each student ticket sells for $7 and each adult ticket sells for $9. There was a total of $543 in revenue from the sale or 67 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.

Answer 1

To determine the number of student and adult tickets sold by the drama club, we define x as student tickets and y as adult tickets. The system of equations is x + y = 67 and 7x + 9y = 543, which represent the total number of tickets and revenue, respectively.

Step-by-step explanation:

To create a system of equations to determine the number of student tickets and adult tickets sold by the drama club, we need to define our variables. Let's let x represent the number of student tickets sold and y represent the number of adult tickets sold. We are given that student tickets cost $7 each and adult tickets cost $9 each, and that the total revenue from 67 tickets sold was $543.

We can set up the following equations:

The first equation will represent the total number of tickets sold: x + y = 67

The second equation will represent the total revenue generated by the ticket sales: 7x + 9y = 543

Thus, our system of equations is:

x + y = 67

7x + 9y = 543

This system can be solved using methods such as substitution, elimination, or matrix operations to find the values of x and y.