Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. Determine the total number of adults and student tickets.

X = number of adults tickets
y = number of students tickets

x + y = 8
7.25x + 5.50y = 52.75

x + y = 8 => y = -x + 8

To find the number of adults tickets:

7.25x + 5.50y = 52.75
7.25x + 5.50( -x + 8 ) = 52.75
7.25x - 5.50x + 44 = 52.75
1.75x + 44 = 52.75
1.75x = 8.75
x = 5

To find the number of students tickets:

x + y = 8
5 + y = 8
y = 3

Answer : There are total of 5 adults tickets and 3 students tickets.