Magnetite iron production

Iron is produced in a blast furnace from iron ore. The wealthiest iron ore is magnetite, which contains 45-70% iron. How much magnetite do we need to get 3 tons of iron?

Final Answer:

a =  4.2857 t
b =  6.6667 t

Step-by-step explanation:

$$\begin{gathered} p_1=70\%=\frac{70}{100}=\frac{7}{10}=0.7 \\ m=3\text{t} \\ a\cdot p_1=m \\ a=m/p_1=3/0.7=4.2857\text{t} \end{gathered}$$

$$\begin{gathered} p_2=45\%=\frac{45}{100}=\frac{9}{20}=0.45 \\ b=m/p_2=3/0.45=6.6667\text{t} \end{gathered}$$

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