i need some help on this word problem please do it for me (12)

The first thing we need to do is identify the important values, our variables, and our equations that model or describe our problem.
• A total of 560 tickets were sold.
• Tickets can be ,A,dult or ,S,tudent
[tex]A+S=560\to(1)[/tex]• The total of tickets sold $3166
,• The value of the Adult ticket is $8
,• The value of the Student ticket is $3.5
[tex]8A+3.5S=3166\to(2)[/tex]We can see that A and S correspond to the number of Adult or Student tickets sold. We solve the equations to find our numbers.
[tex]A=560-S\to\text{(1)}[/tex][tex]\begin{gathered} 8(560-S)+3.5S=3166 \\ 8\times560-8S+3.5S=3166 \\ S(3.5-8)=3166-4480 \\ -4.5S=-1314 \\ S=\frac{-1314}{-4.5} \\ S=292 \end{gathered}[/tex][tex]\begin{gathered} A=560-292 \\ A=268 \end{gathered}[/tex]