## 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 m

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

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3 months 2022-02-03T06:17:12+00:00 1 Answer 0 views 0

He have 47 ducks and 7 cows.

Step-by-step 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 [tex]x.[/tex]

And the number of cows be [tex]y.[/tex]

So, total number of animals are:

[tex]x+y=54[/tex]

[tex]x=54-y[/tex]  ….( 1 )

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

Now, the total number of feet are:

[tex]2(x)+4(y)=122[/tex]

[tex]2x+4y=122[/tex]

Substituting the value of [tex]x[/tex] from equation (1) we get:

[tex]2(54-y)+4y=122[/tex]

[tex]108-2y+4y=122[/tex]

[tex]108+2y=122[/tex]

Subtracting both sides by 108 we get:

[tex]2y=14[/tex]

Dividing both sides by 2 we get:

[tex]y=7.[/tex]

The number of cows = 7.

Now, to get the number of ducks we substitute the value of [tex]y[/tex] in equation (1):

[tex]x=54-y\\x=54-7\\x=47.[/tex]

The number of ducks = 47.

Therefore, he have 47 ducks and 7 cows.