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A spider has 8 legs. A dragonfly has 6 legs and 2 pairs of wings. A cicada has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

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There are Five Spiders, Seven Dragonflies & Six Cicada.

Let X be the number of spiders, Y be number of Dragonflies and Z be number of cicada. Now from the puzzle,
X+Y+Z = 18
8X+6Y+6Z = 118
2Y+Z = 20
Solving this, X=5, Y=7, Z=6