How many horses ?

Gramma ! I went to the zoo today! I saw a lot of horses and chickens.  I counted a total of 57 heads and 176 legs. Now tell me, how many horses did I see?

This is from a long running ad on the local radio, advertising math help.

I only listen to radio when I am driving. The first time I heard it a few years ago. I tried to work this math problem in my head – while behind the wheel.

I heard the ad again a few more times. But I concluded there was not enough information to solve it and that the question was made up to make the ad more interesting.

I head the ad again a few days ago and then recalled it while I was sitting on my desk with access to pen and paper.

I solved it and was very pleased with my self. There were 31  horses and 26 chickens.

I wanted to share my excitement with the world. So I searched to see if anyone else had done it only to find countless other examples with cows, ducks and sheep and horses and chickens but with different numbers.

So, here is my solution to help all you Grandparents and fellow radio listeners out there:

The child counted 57 heads. There were a total of 57 horses and chickens. Each horse and chicken has at least two legs. So, let us attach two legs to each chicken and two legs to each horse:

57 heads × 2 legs = 114 legs attached to all horses and chickens

Number of legs remaining = 176 – 114 = 62 legs

Each horse is missing 2 legs. Therefore the remaining 62 legs must be horses legs. We can use that number to find the number total number of horses:

62 legs ÷ 2 legs per horse = 31 horses

Therefore we also find the number of Chickens by subtracting the number of horses from the total number of 57 heads

57 heads – 31 horses = 26 chickens

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