Question

There is an animal farm where chickens and cows live. All together, there are 82 heads and 192 legs. How many chickens and cows are there on the farm?

Answer 1

There are 14 cows and 68 Chicken in the farm.

Explanation:

A Cow has 4 legs

Chicken has 2 legs.

Lets take there
`x` chickens AND,

there are
`y` number of Cows.

Now we can write two equations for the number of heads and legs.

For the number of heads we can write,

`x+y=82` <--------- 1st equation

For the number of legs we can write,

`2x+4y=192` <------ 2nd equation

We can now solve the simultaneous equations to find
`x` and
`y`

Multiply 1st equation by 2 and deduct it from 2nd equation to remove
`x`

⇒
`2x+4y-2*(x+y)=192-164`

⇒
`2x+4y-2x-2y)=112-164`

⇒
`2y=28`

⇒
`y=14`

Therefore, there are 14 cows in the farm.

Now we can substitute the
`y` value to the 1st equation and find
`x` value.

`x+14=82`

`x=68`

Therefore, there are 68 chickens in the farm.