Problem $1$: Phase Diagram

Consider the sugar$-$water phase diagram below.

$($a$)$ How much sugar will dissolve in $1500$ g water at $90C(194F)?$

$($b$)$ If the saturated liquid solution in part $($a$)$ is cooled to $20C(68F),$ some of the sugar precipitates as a solid. What will be the composition of the saturated liquid solution $($in wt $\%$ sugar$)$ at $20C?$

$($c$)$ How much of the solid sugar will come out of solution upon cooling to $20C?$

Figure $1$ The solubility of sugar $(C_{12}{H}_{22}{O}_{11})$ in a sugar$-$water syrup.