Let s be the number of student tickets and a be the number of adult tickets.
s + a = 85; a = 85 - s
Also,
5s + 10a = 600
Substituting a from the first equation
5s + 10(85 - s) = 600
-5s = -250
s = 50
a = 85 - 50 = 35
The school sold 50 student tickets and 35 adult tickets.
