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