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Terry, BrainBashers best dog groomer noticed that Larry and Harry both had fleas.

If one flea jumps from Larry to Harry, then both will have the same amount.

However, if one flea jumps from the Harry to Larry then the Larry will have 3 times the amount of Harry.

How many fleas do each dog have before any jumping takes place?

Answer: Larry has 5 fleas and Harry has 3 fleas.

Let's say that Larry has L fleas and Harry has H fleas. We have two pieces of information:

"if one flea jumps from Larry to Harry, then both will have the same amount", so:

H + 1 = L - 1         (1)

rearranged gives:

L = H + 2             (2)

"if one flea jumps from the Harry to Larry then the Larry will have 3 times the amount of Harry", so:

L + 1 = 3 x (H - 1)   (3)

We can now use (2) in (3) to give:

L + 1 = 3 x (H - 1)
(H + 2) + 1= 3 x (H - 1)
H + 3 = 3H - 3
6 = 2H
3 = H

and using (2) we can see that L = 5. QED.

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