In farmer Donald's hay loft 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?
[Ref: ZXYL] © Express Newspapers [Author: Mr Stone]
Hint: For every dog, how many chickens and spiders? So how many legs would we have for each dog in total?
There are 17 dogs, 34 chickens and 68 spiders.
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.
Divivde both sides by 40 gives D = 17. Which means there are 34 chickens and 68 spiders. QED.