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

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Answer 1 · 2016-11-12T02:44:57

The farmer has $8$ chickens.

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 $-> x + y = 20$ .

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

Let's start by simplifying the second equation.

$2(2x + y) = 64 -> 2x+ y = 32$

${1} y = 20 - x ->2x + 20 - x = 32$

$x = 12$

$x+ y = 20$

$12 + y= 20$

$y = 8$

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

Hopefully this helps!