Hey Yasmine!

First, we have to start off with finding out how much Fe is in Fe_{3}O_{4} by percentage composition. We can do this by finding out how taking the mass of each individual element in Fe_{3}O_{4} and then dividing by the mass of Fe_{3}O_{4.}

To save time, Fe composes 72.36% and O composes 27.64% of Fe_{3}O_{4}. The question asks for mass of Fe, so we can ignore the percent composition of the Oxygen. To find the minimum mass needed to extract 7.5 kg (or 7500 grams) of Fe, we need to express the 7.5kg mathematically. We know that some amount of Fe_{3}O_{4 }with a percent composition of 72.36% Fe will yield 7.5kg of Fe. Therefore,

(.7236) (x) =7.5kg

Solving for x, we get that we need 10.36kg of Fe_{3}O_{4} in order to get 7.5kg of Fe out of it.

Hope this helped!