I've seen some problem sets given without answers / solutions regarding how to calculate the composition of the mantle given solar composition (and assuming the same would apply to the Earth). For example, the MIT open courseware MOOC has this type of problem in example sheet 1: MIT geology online course.

Given wt% of various substances and factors like how much of the total mass is made up of the core, how do you go about calculating the composition of the mantle. At first pass it seems straightforward but when I actually try to write down some equations and ratios I don't know where to go.

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    $\begingroup$ The question basically says "Here is what the Earth was composed of originally. But the volatiles are gone, and the Iron and a couple of other things are gone from the mantle as well. What is left, and what are their relative abundances?" $\endgroup$ – Wolfgang Bangerth Dec 18 '17 at 4:23

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