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Spiders and Insects
 
Q Once the spiders and the insects played a game of tag. To be fair, the insects were allowed to have more members on their team, because an insect has fewer legs than a spider. (As you know, a spider has eight legs, while an insect has only six.) Altogether, there were 20 heads and 136 legs in the game.

How many insects were playing? How many spiders?


 
A 8 spiders, 12 insects

You know there are 20 animals, and more insects. If all were insects, there would be 120 legs. But there are 136, which means that 16 additional legs must belong to spiders. Since each spider gets 2 of those 16 legs, divide 16 by 2 to get 8 spiders. Subtract 8 from 20 to get 12 insects.

STRATEGY: Work backwards.

Source: Barnes and Noble, 100 Numerical Games, Pierre Berloquin