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.