Bronze, tin and copper

Bronze is an alloy of tin and copper. An alloy of 10% tin and 90% copper is Gunmetal. It is bell metal if it contains 20% tin and 80% copper. How many tons of molten bell metal and copper are needed to make 100 tons of Gunmetal?

Correct answer:

z =  50 t
c =  50 t

Step-by-step explanation:

$$\begin{gathered} m=100\text{t} \\ {p}_1=10\%=\frac{10}{100}=\frac{1}{10}=0.1 \\ {p}_2=90\%=\frac{90}{100}=\frac{9}{10}=0.9 \\ {p}_3=20\%=\frac{20}{100}=\frac{1}{5}=0.2 \\ a=m\cdot p_1=100\cdot 0.1=10\text{t} \\ b=m\cdot p_2=100\cdot 0.9=90\text{t} \\ z\cdot p_3=a \\ z=a/p_3=10/0.2=50\text{t} \end{gathered}$$

$c=m-z=100-50=50\text{t}$

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