The statement of the problem says that, after evaporation, the bag is now 98% water by weight, meaning that the solid matter is now 2% (100% - 98%) instead of t

The statement of the problem says that, after evaporation, the bag is now 98% water by weight, meaning that the solid matter is now 2% (100% - 98%) instead of the 1% it started out as. Per the problem statement, the 100-pound bag was initially 99% = 99 pounds of water. The non-water part (which we'll assume for simplicity was non-volatile solids) was therefore 100 pounds - 99 pounds = 1 pound. Solids don't evaporate, so even after evaporation, the 1 pound of solid matter remains. That 1 pound is now 2% = 1/50 of the weight, per above. The total weight after evaporation is therefore 50 pounds.