Spiders and Beetles
Algebra
Level
pending
A boy collected 8 spiders and beetles into a little box. He counted the legs and found there were altogether 54. How many spiders and how many beetles did he collect?
The answer is 55.
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1 solution
Before you solve this problem you must know how many legs the spider and the beetle have. If you remember your natural science, you know that spiders have 8 legs and beetles 6. Now let us assume that there were only beetles, 8 of them, in the box. That means there should be 6 x 8 = 48 legs, or 6 less than mentioned in the problem. If we substitute one spider for one of the beetles, the number of legs will increase by 2 because the spider has 8 legs and not 6. It is clear that if we substitute three spiders for three beetles we shall bring the number of legs in the box to the required 54. Then instead of 8 beetles we shall have 5, the rest will be spiders. Hence, the boy collected 5 beetles and 3 spiders. Let us verify: 5 beetles ha ve 30 legs and 3 spiders have 24 legs. And 30 + 24 = 54.