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Spiders on the Web

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"Dad, where had you been?" asked Andy.

"I had been to the attic, my son," replied Dad. "And do you know what I saw there? There was a big web with 19 spiders and flies on it."

"How many spiders were there?" asked the little boy with curiosity.

"Well, there were a total of 126 legs on the web," answered Dad with a smile. "Now you can find out how many spiders were there by yourself. Can't you?"

Can you help the little boy find out how many spiders were on the web in the attic?

Answer: 6

Solution:

Assuming 6 legs for each insect, 19 insects will have 114 legs.
But, there are 126 − 114 = 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 = 19; and
8s + 6f = 126.

On solving the above two equations, we get

8s + 6 (19 − s) = 126; or
2s = 126 − (6 × 19).
Thus, s = 6.

Food for thought:

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