Final answer:
The ratio of copper to zinc in the mixture of these two metals is approximately 1 : 4.51.
Step-by-step explanation:
The total mass of the metal in the first mixture is 4 kg. It contains 1/5 copper, which is equal to 1/5 x 4 kg = 0.8 kg of copper. The rest of the mass is zinc, which is 4 kg - 0.8 kg = 3.2 kg of zinc.
The total mass of the metal in the second mixture is 5 kg. It contains 1/6 copper, which is equal to 1/6 x 5 kg = 0.8333 kg of copper. The rest of the mass is zinc, which is 5 kg - 0.8333 kg = 4.1667 kg of zinc.
To find the ratio of copper to zinc in the mixture of these two metals, we add the copper and zinc masses separately. The total mass of copper is 0.8 kg + 0.8333 kg = 1.6333 kg. The total mass of zinc is 3.2 kg + 4.1667 kg = 7.3667 kg. Therefore, the ratio of copper to zinc is 1.6333 kg : 7.3667 kg, which simplifies to approximately 1 : 4.51.