Question

Cindy collects 20 insects for her biology class, all of which are spiders, dragonflies, and cicadas. (Note that a spider has 8 legs and no wings, a dragonfly has 6 legs and 4 wings, and a cicada has 6 legs and 2 wings.) She counts 138 legs and 36 wings altogether. How many cicadas does Cindy collect in total

Answer 1

Cindy collects 4 cicadas in total.

Let,

D represent the number of dragonflies

C represent the number of cicadas

S represent the number of spiders

Since the total number of insects is 20:

Equation 1

D+C+S=20

A spider has 8 legs, a dragonfly has 6 legs, and a cicada has 6 legs. Since the total number of legs is 138:

Equation 2

6D+6C+8S=138

A spider has 0 wings, a dragonfly has 4 wings, and a cicada has 2 wings. Since the total number of wings is 36:

Equation 3

4D+2C+0S=36

Multiplying equation 1 with 6 and subtracting it from equation 2:

6D+6C+8S-6(D+C+S)=138-6(20)

2S=18

S=9

Multiplying equation 1 with 4 and subtracting it from equation 3:

4D+2C+0S-4(D+C+S)=36-4(20)

-2C-4S=-44

Substituting S with 9:

-2C-4(9)=-44

-2C=-8

C=4

Thus, Cindy collects 4 cicadas in total.

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