Answer :
Final answer:
The ratio of copper to zinc in the mixture is calculated by finding the amount of each element in two masses and summing them. The final ratio is derived by converting to grams and simplifying the resulting values. However, the calculated ratio does not match any of the given options, indicating a potential mistake in the options provided.
Explanation:
To find the ratio of copper to zinc in the mixture of two metals, we must calculate the amount of each metal in each of the two given masses and then sum them up.
For the first 4 kg sample containing 1/5 copper and rest zinc:
- Copper = 1/5 of 4 kg = 0.8 kg
- Zinc = 4 kg - 0.8 kg = 3.2 kg
For the second 5 kg sample containing 1/6 copper and rest zinc:
- Copper = 1/6 of 5 kg = 0.833 kg
- Zinc = 5 kg - 0.833 kg = 4.167 kg
Adding up the amounts of each metal from both samples gives us:
- Total copper = 0.8 kg + 0.833 kg = 1.633 kg
- Total zinc = 3.2 kg + 4.167 kg = 7.367 kg
Now converting these masses to grams to make the ratio simpler (since 1 kg = 1000 g):
- Total copper in grams = 1.633 kg * 1000 = 1633 g
- Total zinc in grams = 7.367 kg * 1000 = 7367 g
The ratio of total copper to total zinc in the mixture is 1633:7367, which simplifies to 233:1051 when divided by the greatest common divisor, 7.
The correct answer to the question, "The ratio of Copper and Zinc into the mixture of these two metals", is none of the options listed (a, b, c, d). Therefore, a calculation error may have been made.
