Farmer Ben has only ducks and cows. He can’t remember how many of each he has, but he doesn’t need to remember because he knows he has 22 animals and 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.
Question: Assuming that each animal has all legs intact and no more, how many of each animal does Farmer Ben have?
Your Diagram:

Process: Describe what you did in attempting to solve this problem. Write about such things as:
how you got started
where you got stuck, and how you got unstuck
how you knew when to stop
efforts that didn’t work out or that seemed like a waste of time

Explanation:

- there are many different numbers you can do but if you want to change the numbers and have more ducks then: for every one cow you take away two more ducks.

Step-by-step explanation:

22 total animals

56 total legs

ducks have 2 legs

cows have 4 legs

12 times 4 = 48 ( 12 cows with 4 legs each cow = 48 legs)

4 times 2 = 8 ( 4 ducks with 2 legs each duck = 8 legs)

Answer Link

Fichohgo Fichohgo · Answer 2

Creating a system of equation using the scenario described, the number of cows and ducks owned are 6 and 16 respectively.

Number of legs per cow = 4
Number of legs per duck = 2
Number of ducks = d
Number of cows = c

The equation goes thus :

c + d = 22 - - - (1)

4c + 2d = 56 - - - (2)

From (1)

c = 22 - d - - - - (3)

Substitute (3) into (2)

4(22 - d) + 2d = 56

88 - 4d + 2d = 56

88 - 2d = 56

-2d = 56 - 88

-2d = - 32

d = 16

From (3)

c = 22 - 16

c = 6

Hence, the number of cows and ducks owned are 6 and 16 respectively.

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