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?(1 point) Responses {x+y=7004.5x+2y=1200 {x+y=7002 x+4.5y=1200 {2x+4.5y=12002x−4.5y=700 {x+y=12002x+4.5y=700
The correct system of equations would be:
x + y = 700
2x + 4.5y = 1200
The correct 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 + 4.5y = 1200
The correct system of equations that can be used to find the number of student tickets sold (x) and the number of adult tickets sold (y) in this scenario is:
Equation 1: x + y = 700
Equation 2: 2x + 4.5y = 1200
Let's break down why these equations are the correct choices:
Equation 1 represents the total number of tickets sold. Since the sophomore class sold a total of 700 adult and student tickets, we can express this as x + y = 700, where x represents the number of student tickets and y represents the number of adult tickets.
Equation 2 represents the total revenue generated from ticket sales. We know that adult tickets sold for $4.50 each and student tickets cost $2.00 each. Therefore, to express the total revenue of $1200, we need to multiply the number of adult tickets (y) by $4.50 and the number of student tickets (x) by $2.00, and the sum of these products should equal $1200. This can be written as 2x + 4.5y = 1200.
Thus, the correct system of equations is: x + y = 700 and 2x + 4.5y = 1200.