Two family's decided to go spend the day at the water county water park the smith family purchased 3 adult tickets and one child ticket for a total of $201.the brown family bought 2adult tickets and 3 child tickets for $239, what was the cost of one adult ticket

Adult= $52 Child=$45

We can solve this system of equations through the elimination method.
First we create two equations, with x as the adult tickets and y as the child tickets.
(3x + 1y = 201)
(2x + 3y = 239)

You can now eliminate the x variable from both equations by multiplying them by a number so they become factors of each other.
2(3x+ 1y= 201)
-3(2x+ 3y=239)

Our new equations- We can now remove the x from the equations and solve for y.
(6x+ 2y= 402)
(-6x -9y= -717)

(2y = 402)
+(9y= -717)
= (-7y= -315)
(y=45) So the price of a child ticket is $45.

Pick any of the equations, and replace y with 45 to solve for x.
(3x + 1y = 201)
(3x + 1(45) = 201)
(3x = 156)
x= 52
The price of an adult ticket is $52.