Ring

The gold and copper alloy rings weigh 14.5 g and have a volume of 1.03 cm³. How much gold and copper does each ring contain?
The metal densities are Au 19.3 g/cm³ and Cu 8.94 kg·dm-3

Final Answer:

a =  9.8583 g
c =  4.6417 g

Step-by-step explanation:

$$\begin{gathered} {\rho }_1=19.3{\text{g/cm}}^3 \\ {\rho }_2=8.94{\text{kg/dm}}^3 \\ m=14.5\text{g} \\ V=1.03{\text{cm}}^3 \\ m=\rho V \\ V=m/\rho \\ a+c=m \\ a/{\rho }_1+c/{\rho }_2=V \\ a+c=14.5 \\ a/19.3+c/8.94=1.03 \\ 0.051813a+0.111857c=1.03 \\ Row2-0.051813471502591\cdot Row1\to Row2 \\ 0.06c=0.28 \\ c=\frac{0.27870466}{0.06004335}=4.64172394 \\ a=14.5-c=14.5-4.64172394=9.85827606=9.8583\text{g} \\ a=9.858276 \\ c=4.641724 \end{gathered}$$

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