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. We have all 3 kinds and a total of 18 insects. We have a total of 118 legs and 20 pairs of wings. how many insects do we have of each kind.
Math091: Spiders, Dragonflies and Cicadas
First we would like to solve the problem by simple math,
and then solve it by using algebra.

If all insects are spiders, then we should have 18 x 8 =
144 legs. We have only 118 legs, so the difference is
144 - 118 = 26. Every spider has 2 more legs than the
other insects. We know there should be 26 /2 = 13
dragonflies and cicadas. So we know there are 18 - 13 =
5 spiders.

In the meantime, if all 13 other insects are
dragonflies, then we should have 13 x 2 = 26 pairs of
wings. Because we have some cicadas, we have 26 - 20 = 6
pairs more. Every dragonfly has 1 more pair of wings. So
we know we have 6 / 1 = 6 cicadas and 13 - 6 = 7
dragonflies.