# On a farm there are chickens and cows. Together they have 200 legs and 75 heads. How many cows and chickens are there on the farm? Use a system of equations.

Apr 25, 2018

Number of Cows=25

Number of chicken =50

#### Explanation:

Let the number of cows be $y$ and the number of chicken be $x$

both chicken and cows have 1 head while cows have 4 legs and chicken have 2

Number of Heads = Number of Cows + Number of Chicken

Number of legs = Number of Cows $\times$ 4 + Number of Chicken $\times$2

$75 = y + x$ $\rightarrow \left(1\right)$

$200 = 4 y + 2 x$$\rightarrow \left(2\right)$

$\textcolor{g r e e n}{x = 75 - y}$$\rightarrow$ From (1)

substitute in (2)

$200 = 4 y + 2 \left(75 - y\right)$

$200 = 4 y + 150 - 2 y$

$50 = 2 y$

$y = 25$

$x = 50$