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?

This seems routine enough:

Let

*w*be the number of cows or cows’ heads.

Then 4

*w*is the number of cows’ legs.

Let *c* be the number of chickens or chickens’ heads.

Then 2*c* is the number of chickens’ legs.

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

→ 4

→ 4

→ 2

→

*w*+ 2*c*= 2*w*+ 2*c*+ 84→ 4

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

*w*= 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.