Cows and Ducks Word Problem

Question

Greg wants to know how many cows and ducks are in the meadow. After counting 56 legs and 17 heads, the farmer knows. How many cows and ducks are in the meadow?

Answer 1

Let $C$ be the number of cows, and $D$ the number of ducks. Each animal has just one head (I hope), so $C + D = 17$. On the other hand, each cow has four legs, and each duck has two legs, so $4C + 2D = 56$. Now you have two linear equations in two unknowns. Can you solve for $C,D$?

Answer 2

There are $17$ animals (unless there might be some two-headed cows or something).

If they were all ducks, there would be $34$ legs. Each cow adds 2 extra legs. We need $56-34=22$ extra legs, so there are $11$ cows and $6$ ducks.

Or you can set this up as a simple algebra problem: