Solution:
Assuming 6 legs for each insect, 13 insects will have 78 legs.
But, there are 84 − 78 = 6 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 6 extra legs belong to 3 spiders.
Alternative Solution through Equations:
Let
s be the number of spiders and
f be the number of flies. Then,
s +
f = 13; and
8
s + 6
f = 84.
On solving the above two equations, we get
8
s + 6 (13 −
s) = 84; or
2
s = 84 − (6 × 13).
Thus,
s = 3.
Food for thought:
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