Calculate the fraction of Al$2$O$3$ you would need to add to molten MgO to obtain an $[$Al$2$O$3+$ MgO$]$ slag where the first solidification of $($pure$)$ solid MgO particles occurs at a temperature $50$ K below the melting point of $($pure$)$ solid MgO. State your working hypothesis. Assume the slag is under $1$ bar Ar atmosphere