Answer:
The box office sold 34 general admission tickets and 24 student tickets.
Explanation:
2.5 dollars for students and 3 dollars for general admission.
58 people attended and 162 dollars was collected.
We are asked to find the number of general admission tickets and number of student tickets sold. Let's call the number of general admission tickets sold g and the number of student tickets sold s.
So we are going to make a money equation and a how many equation.
Let's being the money equation: 2.5 per student means you have 2.5*s
and 3 dollars per general admission ticket means you have 3*g. You are given total collected was 162 dollars so 162 is the sum of whatever 2.5s and 3g is. That setup as an equation in symbol form is 162=2.5s+3g
Let's do the how many equation: There are only 2 kinds of tickets, s and g. And we know that the sum of these should be 58 since that is how many people attended. So the equation in symbol form is 58=s+g.
This is our system of equations:
162=2.5s+3g
58= s+ g
------------------I'm going to set this up for elimination by multiplying both equation by -3 which gives:
162=2.5s+ 3g
-174= -3s+-3g
------------------------Now I'm going to add.
-12=-0.5s+0
-12=-0.5s
Divide both sides by -0.5
24=s
Or s=24.
Now we know that s+g=58 and s=24 so g=58-24=34.
The box office sold 34 general admission tickets and 24 student tickets.