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 and child tickets were sold?
Let "a" and "c" represent the numbers of adult and children's tickets sold, respectively. The problem statement tells us two relationships between these values:
... 20a +10c = 15000 . . . . . . total revenue from ticket sales
... c = 3a . . . . . . . . . . . . . . . . relationship between numbers of tickets sold
Using the expression for c, we can substitute into the first equation to get ...
... 20a +10(3a) = 15000
... 50a = 15000
... a = 15000/50 = 300 . . . . . adult tickets sold
... c = 3·300 = 900 . . . . . children's tickets sold
