An alloy consists of 30% zinc, 45% nickel, and the rest copper. Find the weight of copper in 800g of the alloy. Answer: 200g.
The Correct Answer and Explanation is:
Correct Answer:
200 grams of copper
Step-by-Step Explanation:
We are told that an alloy contains:
- 30% zinc
- 45% nickel
- The rest is copper
The total percentage of the alloy is always 100%. To find the percentage of copper, subtract the percentages of zinc and nickel from 100%:
Percentage of copper = 100% – (30% zinc + 45% nickel)
Percentage of copper = 100% – 75%
Percentage of copper = 25%
So, 25% of the alloy is made up of copper.
We are also told the total mass of the alloy is 800 grams, and we are required to find the mass of copper in this alloy.
To calculate the mass of copper:
Mass of copper = (Percentage of copper ÷ 100) × Total mass of alloy
Mass of copper = (25 ÷ 100) × 800 grams
Mass of copper = 0.25 × 800 grams
Mass of copper = 200 grams
Thus, the mass of copper in the alloy is 200 grams.
Additional Explanation:
Alloys are mixtures of metals or metals combined with other elements. The composition is often expressed in percentages, which helps determine the amount of each component in a given total mass.
In this question:
- Percentages must always add up to 100%
- Knowing the percentages of zinc and nickel allows us to easily calculate the percentage of copper
- Once we know the percentage of copper, finding its mass is a straightforward multiplication
This approach can be applied to any similar problem involving percentage composition of alloys or mixtures, provided the total mass and individual percentages are given.
