An alloy consists of nickel, zinc, and copper in the ratio 2:7:9. How many pounds of nickel have to be used to create alloy that contains 4.9lb of zinc
Correct Answer:
1.4 pounds of nickel
Step-by-Step Explanation:
The alloy consists of nickel, zinc, and copper in the ratio 2:7:9. This means for every 2 parts of nickel, there are 7 parts of zinc and 9 parts of copper.
We are told that the amount of zinc in the alloy is 4.9 pounds, and we need to find how many pounds of nickel correspond to that, maintaining the same ratio.
Step 1: Express the ratio
Total parts = 2 (nickel) + 7 (zinc) + 9 (copper) = 18 parts
The zinc part is 7, so:
7 parts → 4.9 pounds of zinc
We need to find how many pounds correspond to 2 parts of nickel.
Step 2: Find the weight per part
If 7 parts = 4.9 pounds, then:
1 part = 4.9 ÷ 7 = 0.7 pounds
Step 3: Find nickel weight
Nickel is 2 parts, so:
Nickel weight = 2 parts × 0.7 pounds per part = 1.4 pounds
Thus, 1.4 pounds of nickel must be used to create the alloy that contains 4.9 pounds of zinc, following the given ratio.
Additional Explanation
In alloy problems where elements are mixed in a certain ratio, the actual weights can vary, but the proportion between the elements remains constant. The ratio tells us the relative amounts, not the absolute amounts.
For example, the ratio 2:7:9 means that for every 2 units of nickel, there are 7 units of zinc, and 9 units of copper. If you know the actual amount of one element, you can calculate the others by setting up a proportion.
This ensures the alloy maintains its intended properties, as the proportions of different metals affect strength, durability, corrosion resistance, and other characteristics.
In summary, using 1.4 pounds of nickel maintains the exact ratio with 4.9 pounds of zinc, ensuring the correct composition of the alloy.
