The sophomore class sold a total of 700 adult and student tickets to the school play. Adult tickets sold $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 create the following system of equations:
$x+y=700$ ($x$ is the number of student tickets sold and $y$ is the number of adult tickets sold)
$2x+4.50y=1200$ ($2x$ is the cost of all student tickets sold, and $4.50y$ is the cost of all adult tickets sold)
Therefore, the system of equations that can be used to find $x$ and $y$ is:
$\begin{cases} x+y=700 \\ 2x+4.50y=1200 \end{cases}$
To set up a system of equations to find the number of student tickets sold (x) and the number of adult tickets sold (y), we can use the following information:
1. The total number of tickets sold is 700, which implies that the sum of the student and adult tickets is 700: x + y = 700.
2. The total revenue from ticket sales is $1,200: 2x + 4.50y = 1,200.
So the system of equations is:
x + y = 700
2x + 4.50y = 1,200
To solve this problem, we need to set up a system of equations using the given information. Let's define x as the number of student tickets sold and y as the number of adult tickets sold.
From the problem, we are given two pieces of information:
1. The total number of tickets sold is 700. So, the first equation is:
x + y = 700
2. The total amount collected from ticket sales is $1,200. Since student tickets cost $2.00 and adult tickets cost $4.50, we can set up the second equation:
2x + 4.50y = 1200
Hence, the system of equations to solve for x and y is:
x + y = 700
2x + 4.50y = 1200