the polar express charges $69.50 per adult ticket and $48.50 per child's ticket. A group of 11 people paid $538.50 for tickets. Which system of equations could be used to fund x, the number of adult tickets purchased, and by, the number of children's tickets purchased?

Let x be the number of adult tickets purchased and y be the number of children's tickets purchased.

The system of equations would be:
1) x + y = 11 (total number of tickets purchased is 11)
2) 69.50x + 48.50y = 538.50 (total cost of tickets is $538.50)

Therefore, the system of equations would be:
x + y = 11
69.50x + 48.50y = 538.50