A sample of bauxite ore is to be cleaned using water in a classifier. The ore particles have a size range of $10$ to $500$ microns. The mixture is being separated into three parts: pure bauxite $($specific gravity $2\mathrm{.}2),$ pure silica $($specific gravity $2\mathrm{.}8)$ and a third fraction is the middling which is recycled. Estimate the range of the three fractions.