# There are 40 cows and chicken in the farmyard. One quiet afternoon, Lack counted and found that there were 100 legs in all. How many cows and how many chickens are there?

Apr 17, 2018

30 Chickens and 10 Cows

#### Explanation:

To help Lack determine how many cows and chickens are on his farm, we can use a system of equations using variables for Chickens and Cows.

Make
Cows = $x$
Chickens = $y$

So $x + y = 40$ the animals on the farm.

For the legs we can make
Cows Legs = $4 x$
Chicken Legs = $2 x$

So $4 x + 2 y = 100$ the legs on the farm.

$x + y = 40$ we can rearrange to $x = 40 - y$
We can plug the value for $x$ into the second equation

$4 x + 2 y = 100$ becomes
$4 \left(40 - y\right) + 2 y = 100$

Distribute the 4 to the parenthesis
$160 - 4 y + 2 y = 100$

Combine like terms
$160 - 2 y = 100$

Use additive inverse to isolate the variable value
$\cancel{160} - 2 y \cancel{- 160} = 100 - 160$

$- 2 y = - 60$

Use multiplicative inverse to solve for the variable
$\frac{\cancel{- 2} y}{\cancel{- 2}} = \frac{- 60}{-} 2$

$y = 30$ there are 30 Chickens

$x = 40 - y$
$x = 40 - 30$
$x = 10$ There are 10 Cows