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:
[tex]21x+38y=5228[/tex]If 44 regular tickets and 58 VIP tickets cost $8792, we can write the following equation:
[tex]44x+58y=8792[/tex]Now, to solve this system of equations, let's solve the first equation for x and then use its value in the second equation:
[tex]\begin{gathered} 21x=5228-38y \\ x=\frac{5228-38y}{21} \\ \\ 44\cdot(\frac{5228-38y}{21})+58y=8792 \\ 10953.9-79.619y+58y=8792 \\ -21.619y=8792-10953.9 \\ -21.619y=-2161.9 \\ y=100 \\ \\ x=\frac{5228-3800}{21} \\ x=\frac{1428}{21} \\ x=68 \end{gathered}[/tex]Therefore the price of a regular ticket is $68 and the price of a VIP ticket is $100.
