Let's denote the price of an adult ticket as "A" and the price of a child ticket as "C."
From the first statement, we have:
3A + 4C = 125
From the second statement, we have:
2A + 3C = 89
We can now solve this system of equations to find the values of A and C.
Multiplying the second equation by 2, we have:
4A + 6C = 178
Now, subtract the first equation from this result:
(4A + 6C) - (3A + 4C) = 178 - 125
A + 2C = 53
We now have a new equation:
A + 2C = 53
Subtracting twice this equation from the second equation:
2A + 3C - 2(A + 2C) = 89 - 2(53)
2A + 3C - 2A - 4C = 89 - 106
-C = -17
Multiplying both sides by -1, we get:
C = 17
Substituting this value of C back into the equation A + 2C = 53:
A + 2(17) = 53
A + 34 = 53
A = 19
Therefore, the price of an adult ticket is $19, and the price of a child ticket is $17.