# A farmer counts his cows and chickens. If he counts 20 heads and 64 feet, how many chickens does he have?

Nov 12, 2016

The farmer has $8$ chickens.

#### Explanation:

We let the number of cows be $x$ and the number of chickens be $y$.

We know that each creature must only have one head, hence we derive our first equation $\to x + y = 20$.

We also know that a cow has 4 feet while a chicken only has $2$. So our second equation is $4 x + 2 y = 64$.

Let's start by simplifying the second equation.

$2 \left(2 x + y\right) = 64 \to 2 x + y = 32$

$\left\{1\right\} y = 20 - x \to 2 x + 20 - x = 32$

$x = 12$

$x + y = 20$

$12 + y = 20$

$y = 8$

So, there are $12$ cows and $8$ chickens.

Hopefully this helps!