three adult and three child movie tickets were purchased for $75
Let the cost of an adult ticket be "A" and the cost of a child ticket be "C".
According to the given information, we can form the following equations:
3A + 3C = 75 (Equation 1)
Since 3 adult and 3 child tickets were purchased, the total cost of the tickets can be found by multiplying the number of adult tickets by the cost of an adult ticket and the number of child tickets by the cost of a child ticket.
Now, let's try solving the equation:
From equation 1, we have 3A + 3C = 75.
Isolating one of the variables, let's solve for A:
3A = 75 - 3C
A = (75 - 3C) / 3
Now, let's substitute this value of A in the equation and solve for C:
3A + 3C = 75
3((75 - 3C) / 3) + 3C = 75
75 - 3C + 3C = 75
75 = 75
The equation holds true for any value of C.
Hence, the cost of an adult ticket and a child ticket cannot be determined with the given information.