Question

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?

Answer 1

Let's call the number of student tickets they sold s, and the number of adult tickets they sold a.
The school sold 50 tickets in all, so a+s=50.
For every adult ticket they sold, they made $3, and for every student ticket, they made $2. So the total amount of money they made is 3a+2s. The problem tells us they made $135, so 3a+2s=135.
a + s = 50
3a + 2s = 135
This is a system of equations. We will proceed by changing the first equation, solving for a(we could solve for s instead, but I decided to solve for a). What this means is we will subtract s from both sides to get a alone.
a + s = 50
a = 50 - s
Now we know what a is(in terms of s, that is), so we can plug it into the second equation.
3a + 2s = 135
3(50 - s) + 2s = 135 (Remember to put the parentheses in!)
150 - 3s + 2s = 135
150 - s = 135
-s = -15
s = 15
This means 15 student tickets were sold. Plug this into one of the original equations to figure out how many adult tickets were sold:
a + s = 50
a + 15 = 50
a = 35
15 student tickets were sold, and 35 adult tickets were sold.