Final answer:
Using a system of equations with two variables representing the price of adult and child tickets and the total ticket sales from two different days, we find that the price of an adult ticket is $7 and the price of a child ticket is $12.
Step-by-step explanation:
The problem given is a system of equations where we are trying to find the cost of an adult ticket and a child ticket based on two days of sales. Let's denote the price of an adult ticket as A and the price of a child ticket as C.
From the first day's sales, we have the equation:
8A + 2C = 80 (1)
From the second day's sales, we have a second equation:
4A + 3C = 64 (2)
We can solve this system of equations using the method of substitution or elimination. We will utilize the elimination method here. First, let's multiply equation (2) by 2 to align the coefficients of A:
8A + 6C = 128 (2')
Now let's subtract equation (1) from modified equation (2'):
8A + 6C - (8A + 2C) = 128 - 80
4C = 48
Divide both sides by 4:
C = 12
Now we know the price of a child ticket. To find the price of an adult ticket, substitute C = 12 into equation (1):
8A + 2(12) = 80
8A + 24 = 80
8A = 56
Divide both sides by 8:
A = 7
Therefore, the price of an adult ticket is $7 and the price of a child ticket is $12.