# 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?

Nov 6, 2015

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 Nov 6, 2015 $a = 200$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 $3 s + 5 a = 1450$, 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 $3 \left(350 - a\right) + 5 a = 1450$. Simplified, that is $1050 + 2 a = 1450$, 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 $s = 350 - \left(200\right)$, and simplifies to $s = 150$.

To check your work, substitute $a$ and $s$ into your original equation and check. $3 \left(150\right) + 5 \left(200\right) = 1450$. That simplifies to $450 + 1000 = 1450 \implies 1450 = 1450$.