The Al$-$Ge phase diagram can be described as a typical binary eutectic system. The melting temperatures for Al and Ge are $656$ and $949$C$,$ respectively. The eutectic temperature is $423$C$.$ The eutectic composition is $55$ wt$\%$ Ge$.$ At the eutectic temperature, the solubility limits can be assumed as follows: Ge in solid $-$Al is $0\mathrm{.}5$ wt$\%$ and Al in solid $-$Ge is $1$ wt$\%.$ Sketch the linearized phase diagram and consider the following: $($a$)$ What phase forms as the pro$-$eutectic one for an Al$-32$wt$\%$Ge alloy? $($b$)$ Determine the alloy compositions for which the equilibrium fraction of the liquid phase is $0\mathrm{.}40$ at $500$C$.($c$)$ What is the equilibrium fraction of the solid phase for a Ge$-5$wt$\%$Al alloy at $800$C$?$