The City Zoo has different admission prices for children and adults. When three adults and two children went to the zoo, the price was $81.22. If two adults and three children got in for $77.18, then what is the price of an adult's ticket and what is the price of a child's ticket?

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.