[tex]x-\ adults\\
y-\ students\\\\ \left \{ {{5x+3.50y=2517.5} \atop {x+100=y}} \right.\\\\
5x+3.5(x+100)=2517.5\\\\
5x+3.5x+350=2517.5\ \ \ | subtract\ 350\\\\
8.5x= 2167,5\ \ \ | divide\ by\ 8.5\\\\
x=255\\\\
y=355\\\\
There\ were\ 355\ student\ tickets\ and\ 255\ adult\ tickets.[/tex]