Spider has eight legs and a dragonfly has six legs. there are 20 spiders and dragonflies altogether. There are 144 legs in all. find the number of spiders, and the number of dragonflies

Answer 1

Let's solve this problem algebraically:

Let x be the number of spiders.
Therefore, the number of dragonflies is 20 - x.

The total number of spider legs is 8x.
The total number of dragonfly legs is 6(20 - x) = 120 - 6x.

The total number of legs is the sum of the spider and dragonfly legs:
8x + 120 - 6x = 144.

Combining like terms, we get:
2x + 120 = 144.

Subtracting 120 from both sides, we have:
2x = 24.

Dividing both sides by 2, we get:
x = 12.

Therefore, the number of spiders is 12, and the number of dragonflies is 20 - 12 = 8.