Heads and Feet (Easy)

In the barnyard there are some cows and some chickens. When asked to count them, Marty came back and said that the number of legs, total, was 84 more than twice the number of heads. So how many of each kind of animal are there?

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This seems routine enough:

Let w be the number of cows or cows’ heads.
Then 4w is the number of cows’ legs.

Let c be the number of chickens or chickens’ heads.
Then 2c is the number of chickens’ legs.

We know 4w + 2c = 2(w + c) + 84

→ 4w + 2c = 2w + 2c + 84
→ 4w = 2w + 84. The c‘s drop out! Huh?
→ 2w = 84
w = 42 cows.

So “84 more” means there are 42 cows, and any number of chickens is possible. Marty, in his clever trickiness, didn’t come up with a complete answer.

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