If we make [tex]a[/tex] an integer that represents the adults that bought tickets, and [tex]s[/tex] the number of students, then we have the equations [tex]a+s=682[/tex], and [tex]a=68+s[/tex].
Using the second equation, we find that [tex]s=a-68[/tex], so we plug this value of [tex]s[/tex] into the first equation to get [tex]a+(a-68)=682[/tex]. We simplify to find [tex]2a=750[/tex]. We divide by [tex]2[/tex] to isolate the desired variable to get [tex]a=\boxed{375\text{ adult tickets were sold}}[/tex].
