Question

Farmer Ben has only ducks and cows. He can't remember how many of each he has. Well, he doesn't need to remember because he knows he has 22 animals and that 22 is also his age. He also knows that the animals have a total of 56 legs, because 56 is also his father's age. Assuming that each animal has all legs intact and no more, how many of each animal does Farmer Ben have?

Answer 1

Farmer Ben has only ducks and cows.

Let the number of ducks is x and number of cows = y

he knows he has 22 animals

Total numbe of ducks and cows = 22

x + y = 22

Number of leg of one duck = 2

Number of legs of x ducks = 2x

Number of legs of a cow = 4

Number of legs of y cows = 4y

the animals have a total of 56 legs

thus , number of legs of x ducks + Number of legs of y cows = 56

2x + 4y = 56

sim[plify

Divide both side by 2

x + 2y = 28

So, the two equations are :

x + y = 22 (1)

x + 2y = 28 (2)

We can solve the system of equation by elimination method :

Subtract equation 2 from ( 1 )

x + 2y - ( x+ y) = 28 - 22

x + 2y - x - y = 6

x - x + 2y - y = 6

0 + y = 6

y = 6

Now, substitute y = 6 in the equation ( 1)

x + y = 22

x + 6 = 22

x = 22 - 6

x = 16

As, x represent the number of ducks, so

Number of ducks = 16

y represent number of cows

Number of cows = 6

Farmer Ben have are 16 ducks and 6 cows

Answer : Farmer Ben have are 16 ducks and 6 cows