Composition of Ore: $F{e}_2{O}_{3}84\%$;$Si{O}_{2}9\%$;$A{l}_2{O}_{3}3\%$;$H_2{O}_4\%$

Composition of Pig Iron: Fe $94\%$; C $3\mathrm{.}8\%$;$Si2\mathrm{.}2\%$

Composition of Flux $CaC{O}_{3}95\%$;$Si{O}_{2}5\%,$ used $50l\frac{b}{100}lb$ pig iron $(22\mathrm{.}68$

$k\frac{g}{45\mathrm{.}36}kg$ pig iron$)$

Composition of Coke C $84\%$;$Si{O}_{2}10\%$;$A{l}_2{O}_{3}3\%$;$H_{2}O3\%,$ used $90l\frac{b}{100}lb$ of pig

iron $(40\mathrm{.}82k\frac{g}{45\mathrm{.}36}kg)$

$,$ Gases: $27\%CO$;$14\%C{O}_2$;$N_{2}59\%$

Assume no iron lost in the slag

Question:

a$.$ The weight of ore smelted, per short ton of pig iron

b$.$ The weight of slag, per ton of pig iron