Question

A farmer looks out into the barnyard and sees the pigs and the chickens. He says to his daughter, "I count 153 heads and 346 feet. How many pigs and how many chickens are out there?"

Answer 1

Answer: There are 20 pigs and 133 chickens.

Step-by-step explanation:

We know that a pig has 4 legs and a chicken has 2 legs.

Let x be the number of pigs and y be the number of chickens , then we have the following system of linear equations:-

$\text{For heads }:\ x+y=153----(1)\\\\\text{For legs }:\ 4x+2y=346---------(2)$

Multiply 2 on both sides of equation (1), we get

$2x+2y=306---------(3)$

Eliminate equation (3) from equation (2), we get

$2x=346-306=40\\\\\Rightarrow\ x=\dfrac{40}{2}=20$

Put x= 20 in (1), we get

$20+y=153\\\\\Rightarrow y=153-20=133$

Hence, there are 20 pigs and 133 chickens.