How Much Does Each Rabbit Weigh?

Date: 10/21/2002 at 07:04:18
From: Mark
Subject: Word puzzle

I am 8 years old and in a junior school.  I have a problem that I 
know the answer to but don't know how it is worked out:

3 Rabbits

Rabbit 1 and Rabbit 2 = 6kg
Rabbit 2 and Rabbit 3 = 9kg
Rabbit 1 and Rabbit 3 = 11kg

The question is how much does each rabbit weigh? I worked out the 
answer but only by guessing. But is there an easy way of working this 
type of problem out?

Thanks

Date: 10/21/2002 at 08:49:51
From: Doctor Ian
Subject: Re: Word puzzle

Hi Mark,

Here's one way to think about it. Suppose Rabbit 2 is actually 
identical twins, exactly the same size and weight. Let's call the 
twins Rabbits 2a and 2b. 

Now, suppose you put all of the following on a scale:

  Rabbit 1, Rabbit 2a, Rabbit 2b, Rabbit 3

How much would they weigh together?  From the first two equations, we 
can see that they should all weigh 15 kg together:

  Rabbit 1, Rabbit 2a, Rabbit 2b, Rabbit 3
  -------------------  -------------------
         6 kg                9 kg
  ----------------------------------------
                  15 kg

But from the third equation, we know that Rabbit 1 and Rabbit 3 weigh 
11 kg together.  So if we take them off the scale, we'll end up with

  Rabbit 2a, Rabbit 2b
  --------------------
         4 kg

This tells you how much Rabbit 2 weighs, and from that, you can find 
the weights of the other rabbits. 

Does this make sense? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/