# You are selling tickets for a high school basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect 1450. How many of each type of ticket did you sell?

##### 2 Answers

150 at $3 and 200 at $5

#### Explanation:

We sold some number,x, of $5 tickets and some number,y, of $3 tickets. If we sold 350 tickets total then x + y = 350. If we made $1450 total on ticket sales, then the sum of y tickets at $3 plus x tickets at $5 needs to equal $1450.

So,

$3y + $5x = $1450

and x + y = 350

Solve system of equations.

3(350-x) + 5x = 1450

1050 -3x + 5x = 1450

2x = 400 -> x=200

y + 200 = 350 -> y=150

#### Explanation:

For this question you can set up a few equations. We'll use the variable

Our equation will be

We can also say

From here, we can substitute

Now that we have

To check your work, substitute