136. The Potato Paradox
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?
Submitted by tartle · Added 15 July 2015
Solution:
Initially, the 100 lbs of potatoes consist of 99% water, meaning they have 1 lb of solid content. When the water content decreases to 98%, the solid content remains the same at 1 lb. To find the new weight, we set up the equation: 1 lb (solid) / (new weight) = 0.02 (2% solids), leading to a new weight of 50 lbs.
Comments (2)
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.
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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