Three hundred gallons of a mixture containing $75$ wt$\%$ ethanol and $25$ wt$\%$ water $($mixture specific

gravity $=0\mathrm{.}877)$ and an unknown quantity of a $40$ wt$\%$ ethanol$60$ wt$\%$ water mixture $($mixture

specific gravity $=0\mathrm{.}952)$ are blended to produce a mixture containing $60$ wt$\%$ ethanol.

a$)$ Do the degree$-$of$-$freedom analysis

b$)$ Calculate the volume of $40$ wt$\%$ ethanol$60$ wt$\%$ water mixture $($V$40)$