A mixture contains 18% copper by weight. How much mixture (in kg) is required to obtain 81 kg of copper?

Options

A. 350
B. 300
C. 450
D. 250

Answer

To solve the problem of how much mixture is required to obtain 81 kg of copper when the mixture contains 18% copper by weight, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the total weight of the mixture that contains 18% copper in order to obtain 81 kg of pure copper.

2. **Set Up the Equation**: If the mixture contains 18% copper, then for every 100 kg of the mixture, there are 18 kg of copper. We can express this relationship mathematically:
\[ \text{Weight of copper} = \text{Percentage of copper} \times \text{Weight of mixture} \]
In this case, we can write:
\[ 81 \text{ kg} = 0.18 \times \text{Weight of mixture} \]

3. **Rearrange the Equation**: To find the weight of the mixture, we can rearrange the equation:
\[ \text{Weight of mixture} = \frac{81 \text{ kg}}{0.18} \]

4. **Calculate the Weight of the Mixture**:
\[ \text{Weight of mixture} = \frac{81}{0.18} = 450 \text{ kg} \]

5. **Conclusion**: Therefore, the total weight of the mixture required to obtain 81 kg of copper is **450 kg**.

### Final Answer:
The mixture required to obtain 81 kg of copper is **450 kg**.

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