Question

A farmer saw some chickens and pigs in a field.

He counted $60$ heads and $176$ legs.

How many chickens and how many pigs did the farmer see?

Answer 1

Find the number of chickens and the number of pigs:

Step 1. Set up the two linear equations:

Let the number of chickens be $x$ and the number of pigs be $y$.

As we know chickens have two legs and pigs have four legs, form the equations:

$x+y=60$ ….(1) [Number of heads counted were $60$]

$\Rightarrow y=60-x$

$2x+4y=176$ ….(2) [Number of legs counted were $176$]

Step 2. Substitute the value of $y$ from equation (1) in equation (2) :

$$\begin{gathered} 2x+4(60-x)=176 \\ 2x+240-4x=176 \end{gathered}$$

Step 3. Solve for $x$:

$\Rightarrow$ $-2x=-64$

$\therefore$ $x=32$

Hence, there were $32$ chickens.

Step 4. Substitute the value of $x$ in the (1) equation to get the value of y:

$$\begin{gathered} 32+y=60 \\ \therefore y=28 \end{gathered}$$

Hence, there were $28$ pigs.

Hence, the number of chickens is $32$ and number of pigs is $28$.