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sweetnsassy_22001
New Member

USA
1 Posts

Posted - 09/04/2007 :  14:58:04  Show Profile
Here is the Game :)

Timothy's balance is wrong: one of the arms is longer than the other. 1 kilogram on the left pan balances 8 melons on the right, wile 1 kilogram on the right pan balances only 2 melons on the left.

If all the melons have the same weight what is it?



1 kilogram = 2.2 lbs

Can anyone help me on this one?
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 09/04/2007 :  15:35:00  Show Profile
Switching the sides means the error factor is going to be 1/2 of what it appears to be. It appears that the melons weigh 1/4 less when switched
In the original weighing, each melon appears to be 1/8 kg. In the second weighing, each melon appears to be 1/2 kg.
note, 1/8 is 1/4 of 1/2
So, the actual error factor is 2 (half of 4). Therefore, one bar is twice as long as the other bar.
You can show this to work out:

1kg 8melons
-------------------- ----------
2x units long ^ x units long

Since the left side is twice as long, it is acting like there is 2kg on the left. Each melon weights 1/4 kg on the above scale.


2melons 1kg
-------------------- ----------
2x units long ^ x units long

Since the left side is twice as long, it is acting like there are 4 melons on the left. Each melon weights 1/4 kg on the above scale.

Edited by - the_hill1962 on 09/04/2007 15:39:11
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 09/04/2007 :  15:50:15  Show Profile
Yes, just call me Over The Hill.
Really, I am not that old but sometimes I feel like it trying to explain math problems.
I had the same problem as you did about showing the solution. So, I put a physical explanation. I thought sweetnsassy_22001 could maybe work from that to come up with the way you showed.
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