Tickets to a movie cost $7.25 for adults and $5.50 for students. a group of friends purchased 8 tickets for $52.75. write a system of equations to represent the situation. how many adult tickets and student tickets were purchased?

Let a = adults  s = students

7.25a + 5.50s = 52.75
a + s = 8
Solve for s
a = 8 - s
7.25(8-s) + 5.50s = 52.75
58 - 7.25s + 5.50s = 52.75
58 - 1.75s = 52.75
-1.75s = -5.25
s = 3
then a must = 5
5 + 3 = 8 is true
7.25(5) + 5.50(3) = 52.75  is true