An alloy composed of nickel, zinc, and copper in a 4:1:2 ratio. How many kilograms of each metal are needed to make 35 kg of this alloy?
The Correct Answer and Explanation is:
To find how many kilograms of each metal are needed in a 35 kg alloy composed of nickel, zinc, and copper in a 4:1:2 ratio:
Step 1: Understand the ratio
The ratio 4:1:2 means:
- 4 parts Nickel
- 1 part Zinc
- 2 parts Copper
Total parts = 4 + 1 + 2 = 7 parts
Step 2: Divide 35 kg into 7 parts
Each part = 35 kg ÷ 7 = 5 kg
Step 3: Calculate the mass of each metal
- Nickel = 4 parts × 5 kg = 20 kg
- Zinc = 1 part × 5 kg = 5 kg
- Copper = 2 parts × 5 kg = 10 kg
✅ Final Answer:
- Nickel: 20 kg
- Zinc: 5 kg
- Copper: 10 kg
Explanation
When dealing with mixtures or alloys made in specific ratios, understanding how to distribute the total mass according to the given ratio is essential. In this case, the alloy is made of nickel, zinc, and copper in the ratio 4:1:2. This ratio doesn’t represent percentages but rather parts by mass. That is, for every 4 parts of nickel, there should be 1 part of zinc and 2 parts of copper, regardless of the total weight of the alloy.
To find out how much of each metal is needed in a 35 kg alloy, the first step is to determine the total number of parts in the ratio. Adding 4 (nickel) + 1 (zinc) + 2 (copper) gives us 7 parts in total. This means the entire alloy is conceptually split into 7 equal portions.
Now, to find the mass of each part, divide the total mass (35 kg) by the number of parts (7), which equals 5 kg per part. From here, multiply each metal’s portion of the ratio by 5 kg to get its actual mass in the alloy. Nickel gets 4 parts, so 4 × 5 = 20 kg. Zinc gets 1 part, so 1 × 5 = 5 kg. Copper gets 2 parts, so 2 × 5 = 10 kg.
This ensures the total mass still adds up to 35 kg and that the internal proportions remain true to the given 4:1:2 ratio. This approach is fundamental in chemistry, metallurgy, and many real-world manufacturing processes where component proportions must be accurately maintained.
