Solution:
Assuming 6 legs for each insect, 18 insects will have 108 legs.
But, there are 122 − 108 = 14 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 14 extra legs belong to 7 spiders.
Alternative Solution through Equations:
Let
s be the number of spiders and
f be the number of flies. Then,
s +
f = 18; and
8
s + 6
f = 122.
On solving the above two equations, we get
8
s + 6 (18 −
s) = 122; or
2
s = 122 − (6 × 18).
Thus,
s = 7.
Food for thought:
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