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Based on the comments and extended chat, this is the kind of question the OP actually wanted to ask: Consider a mixture of Fe and FeO. The total percentage (by weight) of iron is 86.638%. What is the percentage of iron metal in the mixture?
Answer: For simplicity, assume exactly 100 g of the mixture. Hence the total iron is 86.638g and the remaining 13.362g ...
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"The Mn in iron ore should be equal to Mn in slag." vs
"the solution in my book reads MnO from ore equals Mn in hot metal plus MnO in slag."
It seems that the calculation desired involves breaking down the MnO in ore to Mn + O, and putting some of the Mn into the metal; the rest of the Mn goes into slag, as MnO. The hot metal would contain only metallic Mn, ...
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