Central middle school sold 50 tickets for one night at the school play. Student tickets sold for 2$ each and adult tickets sold for 3$ each. They took in 135$. How many of each type of ticket did they sell?
X = Student tickets sold.
Y = Adult tickets sold.
Eq1: x + y = 50 Tickets.
Eq2: 2x + 3y = $135.
Multiply Eq1 by -2 and add the Eqs:
-2x - 2y = -100
2x + 3y = 135
Sum: Y = 35
In Eq1, replace Y with 35:
x + 35 = 50
X = 15
35 adult and 15 student
To find the number of student and adult tickets sold, we can use a system of equations.
Let's assume that x represents the number of student tickets sold and y represents the number of adult tickets sold.
Based on the given information, we can set up the following equations:
1) The total number of tickets sold is 50:
x + y = 50
2) The total revenue from ticket sales is $135:
2x + 3y = 135
We can now solve this system of equations to find the values of x and y.
One way to solve the system is by using the substitution method:
- Solve the first equation for x in terms of y: x = 50 - y
- Substitute this expression for x in the second equation: 2(50 - y) + 3y = 135
- Simplify and solve for y:
100 - 2y + 3y = 135
y = 35
Now that we have found the value of y, we can substitute it back into the first equation to find the value of x:
x + 35 = 50
x = 15
Therefore, Central Middle School sold 15 student tickets and 35 adult tickets.