Farmer brown had ducks and cows. one day she noticed that the animals had a total of 12 heads and 44 feet . how many of the animals were ducks and how many were cows?

Ducks have 1 head and 2 feet, where cows have 1 head and 4 feet.

Let's assume that the farmer has x numbers of ducks and y numbers of cows.

It is known that the animals he was having had the total of 12 heads and 44 feet. So, according of this

x + y = 12 (number of heads)
2x + 4y = 44 (number of feet)

Since, x+y=12, multiplying both side by 2 we get 2x+2y=24, or equivalently 2x=24-2y. Substituting this to the second equation we get

(24-2y) + 4y = 44

So, combining the y terms

24 + 2y = 44

Now substracting 24 from both sides

2y = 44 - 24 = 20

So, dividing both sides by 2

y = 10

So, there were 10 cows that the farmers had. Also, recalling that there was a total of 12 heads, and since the farmer had 10 cows, then there should be 2 ducks.

Thus, the farmer had 10 cows and 2 ducks.