Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.A charitable organization in Livingston is hosting a black tie benefit. Yesterday, the organization sold 21 regular tickets and 38 VIP tickets, raising $5,228. Today, 44 regular tickets and 58 VIP tickets were sold, bringing in a total of $8,792. How much do the different ticket types cost?

Answer 1

Let's use the variable x to represent the price of a regular ticket and the variable y to represent the price of a VIP ticket.

If 21 regular tickets and 38 VIP tickets cost $5228, we can write the following equation:

`21x+38y=5228`

If 44 regular tickets and 58 VIP tickets cost $8792, we can write the following equation:

`44x+58y=8792`

Now, to solve this system of equations, let's solve the first equation for x and then use its value in the second equation:

`\begin{gathered} 21x=5228-38y \\ x=(5228-38y)/(21) \\ \\ 44\cdot((5228-38y)/(21))+58y=8792 \\ 10953.9-79.619y+58y=8792 \\ -21.619y=8792-10953.9 \\ -21.619y=-2161.9 \\ y=100 \\ \\ x=(5228-3800)/(21) \\ x=(1428)/(21) \\ x=68 \end{gathered}`

Therefore the price of a regular ticket is $68 and the price of a VIP ticket is $100.