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a spider has 8 legs, no wings; a dragonfly has 6 legs & 2 pair of wings; a cicada has 6 legs and 1 pair of wings; ?

we have all 3 kinds and a total of 18 insects in a cage; this gives us a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

Posted 268 day ago

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Answers (2)

matherapist 		The set up given in the solution below is correct as are the answers however, the method of solving three equations in 3 unknowns is not given. For this type of problem we use elimination
a) x +y +z=18
b) 8x+6y+6z=118
c) 2y + z=20 Note that this differs slightly from The corresponding tutorsteach solution

eliminate z by subtracting eq c from eq a giving
d) x-y=-2
and multiply eq c by 6 and subtract from eq b giving

e) 8x-6y=-2

Equations d and e are 2 eqns in 2 unknowns which can be solved in a variety of ways but substitution is the easiest. Eq d gives y=x+2 , substitute in eq e and get 8x-6x-12=-2, x=5, plug 5 into eqn e and get y=7; plug these into eqn a to get z=6

Posted 251 day ago

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tutorsTeach 		In this question, presentation or presenting, actually, is very important.
Let's represent each of the insects:
x - would stand for the number of spiders in the cage
y - will stand for the number of dragonfly in the cage
z - represents the number of cicadas we got there
So, x+y+z = 18 --- the number of insects altogether.
The second equation we need here is for each of the body parts:
a spider has 8 legs so it is 8x
a dragonfly has 6 legs, hence 6y
a cicada has also 6 legs, therefore 6z
Let's combine all the legs of those insects: 8x+6y+6z = 118 because 118 is the number of legs altogether
As for the wing pairs, 0x for the spider because it has no wings at all; 2y for the dragonfly because it has 2 pairs of wings; and 1z for the last one, because it has 1 pair of wings.
So, 0x+2y+1z = 20 -- the number of wing pairs total.
So, now we got to ourselves 3 equations - sufficient:
x+y+z = 18
8x+6y+6z = 118
0x+2y+1z = 20
Or:
x+y+z = 18
8x+6y+6z = 118
x+2y+z = 20
After duly solving these equations, you'll get:
y=7
z=6
x=5
If you put those numbers in the 3 equations, you'll get exactly what the problem represents. Questions? Go to TutorsTeach.com and click Find a Tutor.

Posted 267 day ago

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Question Title a spider has 8 legs, no wings; a dragonfly has 6 legs & 2 pair of wings; a cicada has 6 legs and 1 pair of wings; ?
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