Question

Farmer Jones raises ducks and cows. He looks out his window and sees 54 animals with a total of 122 feet. If each animal is “normal”, have many of each type of animal does he have

Answer 1

He have 47 ducks and 7 cows.

Explanation:

Given:

Farmer Jones raises ducks and cows.

He looks out his window and sees 54 animals with a total of 122 feet.

Now, to find the each type of animal he have.

Let the number of ducks be
`x.`

And the number of cows be
`y.`

So, total number of animals are:

`x+y=54`

`x=54-y` ....( 1 )

As, the feet of cows are 4 and ducks are 2.

Now, the total number of feet are:

`2(x)+4(y)=122`

`2x+4y=122`

Substituting the value of
`x` from equation (1) we get:

`2(54-y)+4y=122`

`108-2y+4y=122`

`108+2y=122`

Subtracting both sides by 108 we get:

`2y=14`

Dividing both sides by 2 we get:

`y=7.`

The number of cows = 7.

Now, to get the number of ducks we substitute the value of
`y` in equation (1):

`x=54-y\\x=54-7\\x=47.`

The number of ducks = 47.

Therefore, he have 47 ducks and 7 cows.