Containing 64604

The metal casting consisted of copper and zinc. If we remelted it with 3 kg of pure copper, we would get an alloy containing 80% copper. Instead, we remelted the casting with 3 kilograms of pure zinc, so the resulting alloy contained only 50% copper. Determine the weight of the casting before it is remelted.

Correct answer:

m =  7 kg

Step-by-step explanation:

$$\begin{gathered} m_1=3\text{kg} \\ {m}_2=m_1=3\text{kg} \\ {q}_1=80\%=\frac{80}{100}=\frac{4}{5}=0.8 \\ {q}_2=50\%=\frac{50}{100}=\frac{1}{2}=0.5 \\ q\cdot m+m_1=q_1\cdot (m+m_1) \\ q\cdot m=q_2\cdot (m+m_2) \\ {q}_1\cdot (m+m_1)-m_1=q_2\cdot (m+m_2) \\ 0.8\cdot (m+3)-3=0.5\cdot (m+3) \\ 0.3m=2.1 \\ m=\frac{2.1}{0.3}=7 \\ m=7=7\text{kg} \end{gathered}$$

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