Gold tin alloy

To make a gold decorative item, we alloy 250 g of 18-carat and 200 g of 14-carat gold with tin. How much tin must be added to obtain 14.6-carat gold? Express the purity of the obtained gold in the sense of the applicable legislation.

Final Answer:

x =  50 g

Step-by-step explanation:

$$\begin{gathered} m_1=250\text{g} \\ {k}_1=18/24=\frac{3}{4}=0.75 \\ {m}_2=200\text{g} \\ {k}_2=14/24=\frac{7}{12}\doteq 0.5833 \\ k=14.6/24=\frac{73}{120}\doteq 0.6083 \\ {m}_1\cdot k_1+m_2\cdot k_2=(m_1+m_2+x)\cdot k \\ 250\cdot 0.75+200\cdot 0.58333333333333=(250+200+x)\cdot 0.60833333333333 \\ 0.608333x=30.416667 \\ x=\frac{30.41666667}{0.60833333}=50 \\ x=50=50\text{g} \end{gathered}$$

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