The sophomore class sold a total of 700 adult and student tickets to the school play. Adult tickets sold for $4.50 each, and student tickets cost $2.00 each. If they took in a total of $1,200, which system of equations can be used to find x, the number of student tickets sold, and y, the number of adult tickets sold?
We can start by translating the given information into equations:
Let x be the number of student tickets sold.
Let y be the number of adult tickets sold.
From the problem, we know that the total number of tickets sold is 700:
x + y = 700.....(equation 1)
We also know that the total revenue from tickets sold is $1,200.
The revenue from student tickets is $2.00 multiplied by the number of student tickets sold, which is 2x.
The revenue from adult tickets is $4.50 multiplied by the number of adult tickets sold, which is 4.50y.
So, the total revenue equation is:
2x + 4.50y = 1200.....(equation 2)
Hence, the system of equations that can be used to find x, the number of student tickets sold, and y, the number of adult tickets sold, is:
x + y = 700
2x + 4.50y = 1200
To find the system of equations, we can use the information given in the problem. Let's represent the number of student tickets sold as x and the number of adult tickets sold as y.
From the problem, we know that the total number of tickets sold is 700. Therefore, the first equation is:
x + y = 700
Also, we know that the total revenue from ticket sales is $1,200. The revenue from student tickets is $2.00 times the number of student tickets sold (x), and the revenue from adult tickets is $4.50 times the number of adult tickets sold (y). So the second equation is:
2x + 4.50y = 1200
The system of equations is:
x + y = 700
2x + 4.50y = 1200
To create a system of equations to find the number of student tickets (x) and adult tickets (y) sold, we need to identify the information given in the problem.
Let's assume that x represents the number of student tickets sold and y represents the number of adult tickets sold.
According to the problem:
1) The total number of tickets sold is 700: x + y = 700.
2) The total revenue from ticket sales is $1,200: 2x + 4.50y = 1,200.
Therefore, the system of equations to solve for x and y is:
x + y = 700
2x + 4.50y = 1,200.