Material science-Specification of composition

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The discussion revolves around calculating the weight percentage of germanium (Ge) needed to achieve a specific atom concentration in a silicon (Si) alloy. The initial calculation yielded 72% Ge, but the correct answer is 11.7%. Participants clarify that the problem is from "Materials Science and Engineering Intro" by William D. Callister, specifically question #4.22 in chapter 5. They suggest reviewing question #4.20 for a relevant equation that may help resolve the confusion. Accurate application of the formulas and understanding the context are crucial for solving the problem correctly.
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Im given this problem:
Ge forms a substitutional solid solution with Si. find the weight% of Ge, that must be added to Si to yield an alloy that contains 2.43x10^21 Ge atoms per cubic centimetr. The densities of pure Ge and Si are 5.32 and 2.33 g/cm^3, respectively.

then I have a formula that says C1=(m1/m1+m2)*100% where C1 is the concentration in weight % of material 1 and m1 is the mass of material 1, and m2 is the mass of material 2. I use this formula, and i get 72% for Ge, but the correct answer is 11.7%. does anyone know what i am doing wrong?
 
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Is this problem from Materials Science and Engineering Intro by William D CallisteR?

If it is then it's question # 4.22. Anyway try doing #4.20 first, or just simply use the equation that's given in # 4.20.
 
it is that book, but it is in chapter 5, not chapter 4.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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