A box contains a mixture of small copper spheres and small lead spheres. The total volume of both metals is measured by the displacement of water to be 427 cm³, and the total mass is 4.36 kg. What is the percentage of copper spheres?

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1. Identify the densities of copper and lead. The density of copper is approximately 8.96 g/cm³, and the density of lead is approximately 11.34 g/cm³.
2. Let the volume of copper be V_c and the volume of lead be V_l. We know that V_c + V_l = 427 cm³.
3. Let the mass of copper be m_c and the mass of lead be m_l. We know that m_c + m_l = 4360 g (since 4.36 kg = 4360 g).
4. Using the density formula, \( \text{density} = \frac{\text{mass}}{\text{volume}} \), express the mass of copper as m_c = 8.96 \times V_c and the mass of lead as m_l = 11.34 \times V_l.
5. Substitute the expressions for m_c and m_l into the mass equation: 8.96 \times V_c + 11.34 \times V_l = 4360. Solve the system of equations to find V_c and V_l, then calculate the percentage of copper as \( \frac{V_c}{427} \times 100 \).