Let the price of a children's ticket be x and the price of an adult's ticket be y. We can form a system of equations to solve this problem.
2x + 3y = 81.22
3x + 2y = 77.18
Lets use elimination to solve the system. First, lets multiply the first equation by 3 and the second equation by 2 so the x terms will cancel out.
6x + 9y = 243.66
6x + 4y = 154.36
We can then subtract the equations to cancel out the x variable.
6x + 9y = 243.66
-(6x + 4y = 154.36)
(6x-6x) + (9y - 4y) = (243.66 - 154.36)
0 + 5y = 89.30
Finally, we can find the value of y.
5y = 89.30
y = 17.86
Lastly, we can plug in the value of y and solve for x to find the value of the child's ticket.
2x + 3(17.86) = 81.22
2x + 53.58 = 81.22
2x = 27.64
x = 13.82
Therefore, the child ticket costs $13.82 and the adult ticket costs $17.86.
