Counting spiders from total legs

Question

A farmyard gathering contains chickens (two legs each), cows (four legs each) and spiders (eight legs each). Chickens outnumber cows two to one, and spiders outnumber chickens two to one. Altogether the animals have $440$ legs. How many of them are spiders?

Short answer

44. With $x$ cows there are $2x$ chickens and $4x$ spiders, giving $4x+4x+32x=40x$ legs. So $40x=440$ , $x=11$ , and there are $4\cdot 11=44$ spiders.

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Lessons behind this question

Counting and Combinatorics

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