I don't quite get this concept. An obese individual will have a greater fat content in their body, and thus will have 45% water in their bodies (for example), versus a slim person that will have 75% of body water and a much lower fat level. Is this because fat is made up of about 10% water, so the more fat you have in your body, the more water it "takes up" from the entire body water supply of your body?
Fat mass does not take up water. It brings with it less water percentage than lean mass and so a person with more fat mass will have relatively less % body water. Additional mass as fat contributed relatively less water than additional mass as lean tissue.
Consider a 50 kg individual who is extremely lean. From your numbers, if this individual is 75% water (will will assume lean tissue is 75% water) that is 50 * .75 = 37.5kg water and 12.5kg nonwater body mass.
Now this 50 kg individual puts on 50 kg of fat. The fat is 10% water (from your numbers) so an additional 10 kg of water. This individual its now 47.5kg water and 52.5 nonwater; since this obese person weighs 100 kg now she has 47.5% water, similar to your example.
Suppose instead your 50kg person grew up into a 100 kg performance athlete. Still no fat. She is still 75% water because the lean tissue has 75% water.
It has to do with the % water each type of body mass brings with it. This is with no special knowledge; using just the numbers in your example which is what your professor wants you to use.
All living cells have water content. Fat tissue is made up of living cells, but fat cells have much more triglyceride and lipid content than water content. So fat tissue still has some water content even though it is mostly made of lipids.
An obese person should have more total body water because of this, and also he/she will usually have more muscle mass in the lower body as well. The obese person will have a smaller percentage of water relative to their mass than a lean or muscular person would.