Bowl Scale
A look at what is currently available on eBay
 11lb x 0.1oz / 5Kg x 1g Digital Kitchen Scale w/ Bowl US $9.99 
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 Clear 2lb Mechanical Kitchen Scale with Removable Bowl US $1.25
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 Pink 2lb Mechanical Kitchen Scale with Removable Bowl US $1.25
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 Mantua NFL Super bowl Express Caboose HO scale US $19.99
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 AWS® Premium Digital Bowl Scale + extras 1000 X 0.1g US $39.99
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 AWS® Premium Digital Bowl Scale + extras 1000 X 0.1g US $39.99
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What items do I put on the 3rd scale?
Knowing that the weighting scales 1 and 2 are in equilibrium, which items should be deposited on the left pan of the 3rd scale to make it balanced.
Balance One: 3 Bowls + 1 Cup = 3 Plates + 3 Glasses
Balance Two: 4 Plates + 3 Glasses = 4 Bowls
Balance Three: 3 Bowls = ?
Cup =/= Glass
One: 3B + C = 3P + 3G
Two: 4P + 3G = 4B
Reversing sides of One,
One: 3P + 3G = 3B + C
Two: 4P + 3G = 4B
adding 1 P to both sides of One and combining with Two:
4P + 3G = 3B + C + P = 4B
B = C + P
3B = 3C + 3P
3 Bowls = 3 Cups + 3 Plates.
Checking:
One: 3C + 3P + 1C = 3P + 3G
4C + 3P = 3P + 3G
4C = 3G
Two:
4P + 3G = 4C + 4P
3G = 4C
Same result by substituting in both equations.
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November 22nd, 2006 in
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