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.
Learn more about insects here:
brainly.com/question/14182820
#SPJ4
