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?

equations

solution

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

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.