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Question 622272: Al has collected 60 insects, all of which are spiders,
dragonflies, and cicadas. Al counts 380 legs, and 140
wings altogether. How many insects are there in each
kind?
i want to solve this using equations
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Al has collected 60 insects, all of which are spiders,
dragonflies, and cicadas. Al counts 380 legs, and 140
wings altogether. How many insects are there in each
kind?
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c + d + s = 60 (# of creatures)
6c + 6d + 8s = 380 (# of legs)
2c + 4d = 140 (# of wings)
===============================
2c + 4d = 140 (# of wings)
c + 2d = 70
c = 70 - 2d
-----
Sub for c in eqns 1 & 2
--------
c + d + s = 60 (# of creatures)
70 - 2d + d + s = 60
-d + s = -10
----
6c + 6d + 8s = 380 (# of legs)
6(70 - 2d) + 6d + 8s = 380
420 - 6d + 8s = 380
-3d + 4s = -20
------
-d + s = -10
3d - 3s = 30
-3d + 4s = -20
----------------- Add
s = 10
************
d = 20
**********
c = 30
=================
Dragonflies have 4 wings.
Spiders are not insects.
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