Question

On a farm there are some cows and some chickens if the animals have a total of 40 heads and 112 legs how many cows are there? how many cows are there

and how many chicks are there.how many legs are there and are there really that many legs?

Answer 1

There are 16 cows and 24 chickens 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=40` <--------- 1st equation

For the number of legs we can write,

`2x+4y=112` <------ 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)=112-80`

⇒
`2x+4y-2x-2y)=112-80`

⇒
`2y=32`

⇒
`y=16`

Therefore, there are 16 cows in the farm.

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

`x+16=40`

`x=24`

Therefore, there are 24 chickens in the farm.