Let x be the number of adult tickets and y be the number of student tickets.
From the first sentence we can set up both equations:
1) x + y = 48
2) 7x + 3y = 220
Rearrange #1 to isolate x:
x = 48 - y
Sub that into #2 and solve for y to get your answer:
7(48 - y) + 3y = 220
336 - 7y + 3y = 220
-4y = -116
y = 29
29 student tickets were sold.
