# A farmer has pigs and chickens. She counted 140 eyes and 200 legs. How many pigs and how many chickens were there?

Sep 30, 2016

$\text{The farmer has "30" pigs and "40" chickens.}$

#### Explanation:

Suppose that there are $p$ pigs and $c$ chickens.

Pigs and chickens have $2$ eyes, so, total no. of eyes is $2 p + 2 c .$

The farmer counted $140 \text{ eyes, so, } 2 p + 2 c = 140. \ldots \ldots \ldots \ldots \left(1\right)$

Coming to the count of legs, we have, $4 p + 2 c = 200. \ldots \ldots \ldots \left(2\right)$

$\left(2\right) - \left(1\right) \Rightarrow 2 p = 60 \Rightarrow p = 30.$

Then, by $\left(1\right) , 60 + 2 c = 140 \Rightarrow 2 c = 80 \Rightarrow c = 40.$

$\text{Thus, the farmer has "30" pigs and "40" chickens.}$