A farm raises cows and chickens. the farmer has a total of 42 animals. one day he counts the legs of all animals of his animals and realizes he has a total of 114. how many cows does the farmer have? how many chickens?

Let's call cows x, and chickens as y.

Cows have 4 legs

Chickens have 2 legs.

Let's make two equations from the information they gave us!

x + y = 42

4x + 2y = 114

Now, let's multiply the first equation by 4.

4x + 4y = 168

4x + 2y = 114

Now, subtract the second equation from the first one.

4x - 4x + 4y - 2y = 168 - 114

4y - 2y = 168 - 114

2y = 54

y = 27

Now, plug y = 27 into either equation and solve for x.

x + y = 42

x + 27 = 42

x = 42 - 27

x = 15

There are 15 cows and 27 chickens.