Question

3. A full-price ticket for a college basketball game costs $2.50, and a student ticket costs $1.75. If

tickets were sold, and the total receipts were $1,217.25, how many tickets were student tickets?

Answer 1

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 :)