Question

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?

Answer 1

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

Answer 2

`a = 200` and `s = 150` with Systems of Equations.

Explanation:

For this question you can set up a few equations. We'll use the variable `s` for student tickets, and `a` for adult tickets.

Our equation will be `3s+5a=1450`, for $3 times `s` students, and $5 times `a` students, equal to $1450.

We can also say `s` tickets plus `a` tickets is equal to the amount sold, `350`. `s + a = 350`. From this equation, we can edit it to change it into a system of equations via substitution. Subtract `a` from each side, and we are left with `s = 350 - a`.

From here, we can substitute `s` in to the first equation. We are left with `3(350 - a) + 5a=1450`. Simplified, that is `1050 + 2a = 1450`, and when simplified all the way, it is `a =200`.

Now that we have `a`, we can plug it into our formula for `s`, if you recall, is `s = 350 - a`. That is `s = 350 - (200)`, and simplifies to `s=150`.

To check your work, substitute `a` and `s` into your original equation and check. `3(150) + 5(200) = 1450`. That simplifies to `450 + 1000 = 1450 => 1450 =1450`.