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Farmer Brown had ducks and cows. One day, he noticed that the animals had a total of 12 heads and...

Question:

Farmer Brown had ducks and cows. One day, he noticed that the animals had a total of 12 heads and 44 feet. How many of the animals were cows?

Word Problems

To solve this problem, we need to use the fact that all animals have 1 head. This is the reason why counting the number of heads is equal to counting the number of animals present. The number of feet, though, varies.

Answer and Explanation:


Let the number of cows be c.

Each animal has one head. This means that the number of heads is equal to the number of animals on the farm. Also, there are c cows. At the same time, 12 total heads mean that there are 12 total animals. As c out of 12 are cows, the number of ducks is 12-c.

Now, cows have 4 feet each. The total number of cow feet on the farm is 4c. Ducks have 2 feet each. The total number of duck feet is 2(12-c). The total number of feet is 44. So,


$$\begin{align} 2c+4(12-c)&=44\\ 2c+48-4c&=44\\ -2c&=44-48\\ c&=\frac{-4}{-2}\\c&=2 \end{align} $$


Thus, there are 2 cows.


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