Beetles and Spiders
Naval collected 8 spiders and beetles into a little box. When he counted the legs he found that there were altogether 54.
How many beetles and how many spiders did he collect?
How many beetles and how many spiders did he collect?
An essential fact we must know before we start solving the problem, we must know how many legs the spider and the beetle have. From the study of natural science, we know that spiders have 8 legs and beetles 6.
Let us now assume that there were only beetles in the box - 8 of them. Then there should be 48 legs, or 6 less than mentioned in the problem.
Now 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 now clear that if we substitute three spiders for three beetles we shall bring the number of legs in the box to the required 54. In that case, instead of 8 beetles we shall have 5. The rest will be spiders.
Now we can conclude that the boy collected 5 beetles and 3 spiders: 5 beetles have 30 legs and 3 spiders have 24 legs. In all the boy collected 54 legs.
Let us now assume that there were only beetles in the box - 8 of them. Then there should be 48 legs, or 6 less than mentioned in the problem.
Now 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 now clear that if we substitute three spiders for three beetles we shall bring the number of legs in the box to the required 54. In that case, instead of 8 beetles we shall have 5. The rest will be spiders.
Now we can conclude that the boy collected 5 beetles and 3 spiders: 5 beetles have 30 legs and 3 spiders have 24 legs. In all the boy collected 54 legs.
