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Mathematical Puzzles
The Potato paradox

 
Thu Jul 16, 2015 6:38 am  by tartle

Fred brings home 100 lbs 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?
 
   
Tue Jul 21, 2015 9:51 am  by n4blue

The new weight is 50 lbs.

If 99% of 100 lbs is water, then the non-water component weighs 1 lb.

The next day they have dried out, so 98% is water, 2% is non-water. If the 2% weighs 1 lb then the whole lot weighs 50 lbs.
 
   
Thu Jul 14, 2016 2:51 pm  by bathfilms

100lbs = 1lb starch + 99lb Water

When you dry off some of the water, the starch content is still 1lb

So the new composition is simply:

Using L = loss of water in lbs
W = original total water

(W - L)/(100 - L) = 0.98

(99 -L)/(100 - L) = 0.98

99 - L = 0.98x(100 - L)

99 - L = 98 - 0.98L

99 - 98 = L - 0.98L

1 = 0.02L

L = 1/0.02 = 50

So the new weight = 100 - 50 = 50 lbs
 
   
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