Potato paradox: Difference between revisions
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One explanation begins by saying that initially the non-water weigh is 1 pound, which is 1% of 100 pounds. The one asks: 1 pound is 2% of how many pounds? In order that that percentage be twice as big, the total weight must be half as big. |
One explanation begins by saying that initially the non-water weigh is 1 pound, which is 1% of 100 pounds. The one asks: 1 pound is 2% of how many pounds? In order that that percentage be twice as big, the total weight must be half as big. |
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An explanation via algebra is as follows. |
An explanation via algebra is as follows. |
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The weight of water in the fresh potatoes is <math>0.99 * 100</math>. |
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If <math>x</math> is the weight of water lost from the potatoes when they dehydrate then <math>0.98(100 - x)</math> is the weight of water in the dehdrated potatoes. Therefore |
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Expanding brackets and simplifying |
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: <math>99 - (98 - 0.98x) = x</math> |
: <math>99 - (98 - 0.98x) = x</math> |
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: <math>1 + 0.98x = x</math> |
: <math>1 + 0.98x = x</math> |
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Subtracting the smaller <math>x</math> term from each side |
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: <math>1 + 0.98x - 0.98x = x - 0.98x</math> |
: <math>1 + 0.98x - 0.98x = x - 0.98x</math> |
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: <math>1 = 0.02x</math> |
: <math>1 = 0.02x</math> |
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And solving |
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: <math>1 / 0.02 = 0.02x / 0.02</math> |
: <math>1 / 0.02 = 0.02x / 0.02</math> |
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Which gives the lost water as |
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: <math>50 = x</math> |
: <math>50 = x</math> |
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And the dehydrated weight of the potatoes as |
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: <math>100 - x = 100 - 50 = 50 </math> |
: <math>100 - x = 100 - 50 = 50 </math> |
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Revision as of 20:41, 13 August 2013
The potato paradox is a mathematical calculation that results in an un-intuitive result.
Description
The paradox has been described as:[1]
You have 100 pounds of Martian potatoes, which are 99 percent water by weight. You let them dehydrate until they’re 98 percent water. How much do they weigh now?
The Universal Book of Mathematics states the problem as follows:[2]
- Fred brings home 100 pounds of potatoes, which (being purely mathematical potatoes) consist of 99 percent water. He then leaves them outside overnight so that they consist of 98 percent water. What is their new weight? The surprising answer is 50 pounds.
It is not really a paradox, but most people find the answer counter-intuitive.[3]
Explanation
One explanation begins by saying that initially the non-water weigh is 1 pound, which is 1% of 100 pounds. The one asks: 1 pound is 2% of how many pounds? In order that that percentage be twice as big, the total weight must be half as big.
An explanation via algebra is as follows.
The weight of water in the fresh potatoes is .
If is the weight of water lost from the potatoes when they dehydrate then is the weight of water in the dehdrated potatoes. Therefore
Expanding brackets and simplifying
Subtracting the smaller term from each side
And solving
Which gives the lost water as
And the dehydrated weight of the potatoes as
References
External links
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