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/ |
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