Question

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?

Answer 1

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