The ballpark made a total of $15,000 from ticket sales at wednesday's game. the ballpark charges $20 for each adult ticket and $10 for each child's ticket. they sold 3 times as many children's tickets as adult tickets. write a system of equations that can be used to determine the number of adult and child tickets sold. how many adult tickets and child tickets were sold?

Assume that the number of adult tickets is a and the number of child tickets is c.

We are given that the adult ticket is sold for 20$, the child ticket is sold for 10$ and that the total is $15,000. This means that:
20a + 10c = 15,000 > equation I

We are also given that number of child tickets is 3 times that of adult's. This means that:
c = 3a > equation II

Substitute with equation II in equation I to get a as follows:
20a + 10c = 15,000
20a + 10(3a) = 15,000
20a + 30a = 15,000
50a = 15,000
a = 300 tickets

Substitute with the value of a in equation II to get c as follows:
c = 3a
c = 3(300)
c = 900 tickets

Based on the above calculations,
number of child tickets = 900 ticket
number of adult tickets = 300 ticket