$(25$ points$)$

Water is used to extract acetone from an ethyl$-$acetate and acetone mixture. Locate the following points on the ternary diagram:

$($a$)$ Mixture containing $30kg$ of acetone and $70kg$ of ethyl$-$acetate

$($b$)10wt\%$ acetone, $2wt\%$ water $($point D$)$

$($c$)90wt\%$ water, $5wt\%$ acetone $($point $F)$

$($d$)$ If $50kg$ of a $10wt\%$ acetone, $2wt\%$ water solution $($point $D$ above$)$ is mixed with $80kg$ of $90wt\%$ water, $5wt\%$ acetone solution $($point $F$ above$),$ what will be the final composition of the composite mixture $($point M$)?$ Plot the point M on the ternary diagram.