re: How much would 100lbs of potatoes @ 99% water weigh after they dry to 98% water?

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Potato Paradox Wiki Article

You actually had me thinking about how to calculate this!

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Interesting. Did not think of it like that.

Do your own homework.

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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? The surprising answer is 50 lbs.

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Why?

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100 lbs of potatoes, 99% water (by weight), means that there's 99 lbs of water, and 1 lb of solids. It's a 1:99 ratio.

If the water decreases to 98%, then the solids account for 2% of the weight. The 2:98 ratio reduces to 1:49. Since the solids still weigh 1 lb, the water must weigh 49 lbs.

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Someone posited that:
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100 lbs of potatoes, 99% water (by weight), means that there's 99 lbs of water, and 1 lb of solids. It's a 1:99 ratio.

If the water decreases to 98%, then the solids account for 2% of the weight. The 2:98 ratio reduces to 1:49. Since the solids still weigh 1 lb, the water must weigh 49 lbs.
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100 lbs of potatoes, 99% water (by weight), means that there's 99 lbs of water, and 1 lb of solids. THIS IS TRUE
If the water decreases to 98%, then the solids account for 2% of the weight. The 2:98 ratio reduces to 1:49. Since the solids still weigh 1 lb, the water must weigh 49 lbs. THIS IS NOT TRUE. The solid still weighs 1 lb, that’s true…what’s NOT true is that the solid is now 2% of the 100lbs…IF 99% equaled 99lbs, how could you possibly think that 98% equaled 49lbs? You’re saying that 100lbs of potatoes dried out a little, and lost HALF their weight?

So, let’s think about this….
If a potato is 99% water, then 100 lbs of potatoes contains 99 lbs of water and 1 lb of other material. For the potatoes to dry down to 98% water, we’ll need to understand that the solid portion still weighs 1 lb, but the 99 lbs of water is going to decrease…
The 1 lb of solid material remains, but the moisture content is reduced from 99% to 98%.
So the question is, if 99% equaled 99lbs of water, what does 98% weigh?

Which can be expressed as 99pct/99 lbs = 98pct/x lbs, cross multiply and we get 99x = 98 x 99, which equates to 99x=9702, which is expressed as x=9702/99, which equals 98… as in 98 lbs. And we still have our 1 lb of solid material, so our slightly drier potatoes now weigh in at 99 lbs instead of their previous 100 lbs!