SOLUTION: A full-price ticket for a college basket ball game costs $2.50 and a student ticket cost $1.75. IF the 585 tickets were sold, and the total receipts were $1,217.25, HOW MANY WERE S

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Question 162048: A full-price ticket for a college basket ball game costs $2.50 and a student ticket cost $1.75. IF the 585 tickets were sold, and the total receipts were $1,217.25, HOW MANY WERE STUDENT TICKETS?
Answer by schrammbledeggs(41) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say x = full price tickets
Let's say y = student tickets

We can write two equations:
From "585 tickets were sold" we can make the equation:
x + y = 585


And from "Full-price ticket is $2.50 and student ticket is $1.75 and total receipts is $1,217.25"...we can make the equation:
2.50x + 1.75y = 1,217.25

So now we can use substitution to find our answer...since we only have to find how many student tickets...we will solve the first equation for x so we can plug that into the 2nd equation to solve for y.

x + y = 585
x + y - y = 585 - y
x = 585 - y

Now we plug that into our 2nd equation:
2.50 (585 - y) + 1.75y = 1217.25


Distribute your 2.50
1462.5 - 2.50y + 1.75y = 1217.25

Add the y's:

1462.5 - 0.75y = 1217.25

Subtract 1462.5 from both sides:

1462.5 - 0.75y - 1462.5= 1217.25 - 1462.5
-0.75y = -245.25

Divide both sides by -0.75:
y = -245.25/-0.75
y = 327
There were 327 student tickets :)