There are 2 spiders, 5 dragonflies, and 4 birds.

Step-by-step explanation:

Word Problem

Let us analyze the given problem.

What is asked?

The problem is asking for the number of spiders, dragonflies, and birds.

Given:

number of a spider's legs - 8 legs

number of a dragonfly's legs - 6 legs

number of a bird's legs - 2 legs

number of a dragonfly's wings - 2 pairs

number of a bird's wings - 1 pair

total number of heads - 11

total number of legs - 54

total number of pairs of wings - 14

Equations:

Let x be the number of spiders.

Let y be the number of dragonflies.

Let z be the number of birds.

x + y + z = 11

8x + 6y + 2z = 54

2y + z = 14

Solution:

Multiply 8 to the first equation to eliminate x. Then subtract the second equation from it.

8(x + y + z = 11) = 8x + 8y + 8z = 88

8x + 8y + 8z = 88

- 8x + 6y + 2z = 54

2y + 6z = 34

Now, subtract the third equation from it.

2y + 6z = 34

- 2y + z = 14

5z = 20

5z/5 = 20/5 (Divide both sides by 5.)

z = 4

There are 4 birds.

Plug in the number of the birds from the third equation to find the number of dragonflies.

2y + z = 14

2y + 4 = 14

2y = 14 - 4

2y = 10

2y/2 = 10/2 (Divide both sides by 2.)

y = 5

There are 5 dragonflies.

Next, plug in the values of y and z to the first equation to find the number of spiders.

x + y + z = 11

x + 5 + 4 = 11

x + 9 = 11

x = 11 - 9

x = 2

There are 2 spiders.

Final Answer:

2 spiders

5 dragonflies

4 birds

Checking:

To check if the answers are correct, plug in the values of x, y and z to the second equation.

8x + 6y + 2z = 54

8(2) + 6(5) + 2(4) = 54

16 + 30 + 8 = 54

54 = 54 ✔

For examples of word problems involving the number of heads and legs, visit the links:

brainly.ph/question/1920654

brainly.ph/question/549987

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Verified answer

Answer:

8 spider

2 dragon fly

5 birds