Spider(s) on the Web

Algebra Level 2

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

"I had been to the attic, my son," replied Dad. "And do you know what I saw there? There was a big web with 12 spiders and flies on it."

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

"Well, there were a total of 86 legs on the web," answered Dad with a smile. "Now you can find out how many spiders were there by yourself. Can't you?"

How many spider(s) did the little boy find on the web in the attic?

Note: Spiders have 8 legs and flies have 6 legs.


The answer is 7.

Lew Sterling Jr by Lew Sterling Jr , 24, USA

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2 solutions

Rama Devi
Jun 4, 2015

s + f = 12; and

8s + 6f = 86.

On solving the above two equations, we get

8s + 6 (12 − s) = 86; or

2s = 86 − (6 × 12).

2s = 86 - 72

2s = 14

s = 7

Therefore the number of spiders in the web is 7.

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Lew Sterling Jr
Feb 5, 2015

Solution:

Assuming 6 legs for each insect, 12 insects will have 72 legs.

But, there are 86 − 72 = 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 = 12; and

8s + 6f = 86.

On solving the above two equations, we get

8s + 6 (12 − s) = 86; or

2s = 86 − (6 × 12).

2s = 86 - 72

2s = 14

s = 7

Thus, s = 7.

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