# Nice Legs

In Old McDonald’s farm there are a number of chickens, dogs and spiders. There are twice as many chickens as there are dogs and there are twice as many spiders as chickens. Altogether there are 680 legs. How many dogs are there?

### 2 guesses to Nice Legs

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• Paul

Since the spiders’ would have 32 legs (4 spiders) to the chickens’ 4 legs (2 chickens) and the dog’s 4 legs (1 dog), the number of dog legs and chicken legs combines would be 25% the total number of spider legs, and the number of dogs would be 25% of the number of spiders and the number of chickens would be in between. As a result there would be 68 spiders (544 legs), 34 chickens (68 legs) and 17 dogs (68 legs).

• Dude

You are absolutely correct!

If there were D dogs, we would have 2D chickens. Which means we have 2 x 2D = 4D spiders.

How many legs would we have?

D dogs have 4D legs.
2D chickens have 4D legs.
4D spiders have 32D legs.

So in total we have 4D + 4D + 32D = 40D legs.

We know that we have 680 legs in total, so 40D = 680.

Divide both sides by 40 gives D = 17 dogs. (Which means there are 34 chickens and 68 spiders.)

You’re today’s winner.