Question

Farmer Ben has only ducks and cows. He can't remember how many each he has, but he really doesn't need to remember. He does know that he has 22 animals, which is his age. He also remembers that those animals have a total of 56 legs, which is his father's age. Assuming that each animal is normal, how many of each does Farmer Ben have?

Answer 1

Suppose he's got D ducks and C cows. Then we know that D + C = 22.
Now: a duck has two legs, and a cow has four. So 2D + 4C = 56, which is the total number of legs. But D + C = 22, so 2D + 2C = 44. So if you subtract this equation from the one that tells you the number of legs, you'll get 2C = 56-44 = 12, so C = 6. But D + C = 22, so D = 16.
Check it: If C = 6 and D = 16, then D + C = 22, and 2D + 4C = 32 + 24 = 56. Correct.

Answer 2

16