How do I solve this problem on mass balance from blast furnace iron making?
"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, not MnO. It shouldn't be a huge adjustment in the answers.