Solution:
Assuming 6 legs for each insect, 21 insects will have 126 legs.
But, there are 138 − 126 = 12 extra legs.
It is important to note that spiders have 8 legs and flies have 6 legs. So, there are 2 extra legs per spider on the web.
Thus, the 12 extra legs belong to 6 spiders.
Alternative Solution through Equations:
Let
s be the number of spiders and
f be the number of flies. Then,
s +
f = 21; and
8
s + 6
f = 138.
On solving the above two equations, we get
8
s + 6 (21 −
s) = 138; or
2
s = 138 − (6 × 21).
Thus,
s = 6.
Food for thought:
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