I was helping my GF with this and we cant figure it out. so:

*From 50t or iron ore containing Fe2O3 and Fe3O4 is made 35,7t of Fe. How many tonnes of Fe*_{2}O_{3} and) Fe_{3}O_{4} are in ore (their ratio)?

We are assuming that the ore contains no impurities and the process of smelting ore is has 100% yield.

So the book say that its 29t of Fe_{3}O_{4} and 21t of Fe_{2}O_{3}.(which doesnt even make the amount of pure iron which is in the written in the task)

But I counted something totaly different, im not sure if Its correct:

mass fraction of Fe in Fe_{2}O_{3} is 0,6994, in Fe_{3}O_{4} is 0,723

W1 is mass fraction of Fe_{2}O_{3} in 50t of ore, W2 is same for Fe_{3}O_{4}

w1+w2=1 -> w1=1-w2

50*0,6994*w1 + 50*0,723*w2 = 35,7

34,97*(1-w2) + 36,15w2 = 35,7

36,15w2 - 34,97w2 = 35,7 - 34,97

1,18w2 = 0,73

w2=0,686

m( Fe_{3}O_{4}) = 0,686*50=30,93t

m( Fe_{2}O_{3})= 50-30,93 = 19,067t

So did I counted right or made some mistake somewhere ? thanks