How many tons of ore are needed to make 1.00 ton of iron if the % recovery of iron from the ore is 91.5%?

Question

One of the ores of iron is hematite, Fe2O3, mixed with other rock. One sample of this ore is 31.4% hematite. How many tons of this ore are needed to make 1.00 ton of iron if the percent recovery of iron from the ore is 91.5%? 1 ton = 2000 lbs.

Answer 1

using the molar masses of 159.69 g/mol  Fe2O3 &  55.845 g/mol Fe, find mass of hemitite with 1 ton of iron:

1 ton Fe @ 159.69 tons Fe2O3 / (2)(55.845tons Fe) = 1.43 tons of Hemitite

find tons of hemitite needed for 1 ton Fe, if their is only 91.5 % recovery:

1.43 tons of Hemitite @ 100 / 91.5 = 1.56 tons Fe2O3

find tons of rock if it is only 31.4% hemitite:

1.56 tons Fe2O3 @ 100 / 31.4 = 4.98 tons

your answer is 4.98 tons of rock