Kyle's family bought 4 adult tickets and 2 student tickets for $52. maria's family bought 3 adult tickets and 5 student tickets for $60. how much does each type of ticket cost?

Adult tickets cost $10 each and student tickets cost $6 each.

Given:
Kyle's family bought 4 adult tickets and 2 student tickets for $52
Maria's family bought 3 adult tickets and 5 student tickets for 60.

Let us assign x as the adult tickets and y as the students tickets

Kyle's family:  4x + 2y = 52
Maria's family: 3x + 5y = 60

Let us find the value of x using Kyle's equation:
4x + 2y = 52
4x         = 52 - 2y
  x         = (52 - 2y)/4
  x         = 13 - y/2
Substitute the value of x in Maria's equation to find y.
3x + 5y = 60
3(13 - y/2) + 5y = 60
39 - 3y/2 + 5y = 60
     - 3y/2 + 5y = 60 - 39
     - 3y/2 + 5y = 21
  2(-3y/2 + 5y) = 2(21)
     -3y + 10y = 42
               7y = 42
           7y/7 = 42/7
                y = 6

x = 13 - y/2
x = 13 - 6/2
x = 13 - 3
x = 10

To check:
Kyle's Family                      Maria's Family
4x + 2y = 52                        3x + 5y = 60
4(10) + 2(6) = 52                  3(10) + 5(6) = 60
40 + 12 = 52                        30 + 30 = 60
52 = 52                                 60 = 60