$100$ ton of coal is burned to produce $15$ ton ash. The coal is damp $(0\mathrm{.}3\%$ moisture, on a mass basis$)$ and it is burned with air that has $7\%$ moisture in it $($mass basis$).$ The outlet gas composition $($dry basis$)$ is $12\%C{O}_2,5\%CO,79\%N_2,1\%S{O}_2,3\%O_2.$ Solve for the coal composition in mass fractions $C,H,S,$ moisture and ash.