Central Middle School sold 50 tickets for one night of 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?

number of student tickets --- x

number of adult tickets === 50 - x

solve for x

2x + 3(50-x) = 135

30 20

25 adult and 15 student

35 adult and 15 student

Neither me nor my teacher could figure this out. I think this question is rigged.

To determine the number of student tickets and adult tickets sold, we can use a system of equations to solve for the variables.

Let's assume the number of student tickets sold to be 'x' and the number of adult tickets sold to be 'y'.

According to the given information, we know that:

1. The total number of tickets sold is 50: x + y = 50.

2. The total amount earned from the ticket sales is $135: 2x + 3y = 135.

To solve this system of equations, we can use the substitution or elimination method.

Let's solve using the elimination method:
- Multiply the first equation by 2 to match the coefficient of 'x' in the second equation: 2(x + y) = 2(50) becomes 2x + 2y = 100.
- Subtract the second equation from the first equation to eliminate 'x': (2x + 2y) - (2x + 3y) = 100 - 135.
Simplifying, we get: -y = -35.

Divide both sides of the equation by -1 to solve for 'y': y = 35.

Substitute the value of 'y' back into the first equation to solve for 'x': x + 35 = 50 => x = 50 - 35 = 15.

Therefore, Central Middle School sold 15 student tickets and 35 adult tickets.