Answer:
Adult: 59 tickets, Student: 642 tickets
Step-by-step explanation:
$5 = ticket per student (s)
$8 = ticket per adult (a)
$3682 = total money made
# of s = 11a-7 (7 less than 11 times the adults)
We can use this information to create a systems of equations.
5s + 8a = 3682
*price of a ticket times the number of students or adults equals total*
where s = 11a-7
Now we substitute in:
5(11a-7) + 8a = 3682
55a - 35 + 8a = 3682
63a - 35 = 3682
63a = 3717
a = 59
so 59 adult tickets were sold, now we can use this information to solve for student tickets.
s = 11(59)-7
s = 642
So 59 adult tickets, and 642 student tickets were sold.
. (Integration along the 
axis would be way easier, but whatever)