Question: Suppose a person weighing 530 Newtons is floating in a salt lake (concentration of 20% NaCl) with a specific gravity of 1.148. How much less of the person's body would be in the salt water as compared to if he were floating in ordinary water (w/ density 1.00g/cm^3)? Comment: One answer people keep giving me is that the weight "lost" is equal to the difference in specific gravities multiplied by the original weight. It doesn't seem obvious to me why someone would draw such a conclusion. I understand from Archimede's Principle that, as a result of the saltwater being more dense than ordinary water, less water must be displaced in order to balance the constant downward force mg of the person. However, I am having trouble expressing this mathematically.