# Does the Potato Problem assume 1% water = 1 lb of water?

The Universal Book of Mathematics states the problem without saying anything of the mass of water or potatoes:

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.

Thus I understand Method 1, but not 2 quoted beneath:

100 lb of potatoes, 99% water (by weight), means that there's 99 lb 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 lb for a total of 50 lbs for the answer.

Doesn't Method 2 assume that 99% of water = 99 lb of water? How do we know that 1% water by weight = 1 lb of water?

I have a BA in Economics, and already know elementary algebra.

• What is 1% of 100 lb? – Wojowu Jan 22 at 21:16
• @Wojowu 1 lb, obviously. But how's this relevant? – Pamela Lee Jan 22 at 21:16
• 1% of water by weight means that 1% of weight is water. 1% of weight is 1 lb, hence 1 lb of water. – Wojowu Jan 22 at 21:18
• These percentages are explicitly stated as by weight. That's the answer to your question. – Ethan Bolker Jan 22 at 21:19

As the original potatoes are $$99\%$$ water, the $$100$$ lbs must be split as $$1$$ pound solid potato flesh and $$99$$ pounds water. Now, the solid potato flesh does not evaporate so you'll always have $$1$$ pound of solid potato flesh. Post evaporation we must have $$x$$ pounds of water where $$\frac x{x+1}=.98\implies x =.98x +.98\implies .02x=.98\implies x =49$$ Thus at the end we must have $$49+1=50$$ pounds of combined water and solid potato flesh.
• What on earth do you imagine $99\%$ of $100$ pounds might mean? – lulu Jan 22 at 21:31