A ore contains 12% copper how many kilograms of the ore are required to get 69 kg of copper

Answer

To solve the problem of how many kilograms of ore are required to obtain 69 kg of copper when the ore contains 12% copper, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Percentage**:
The ore contains 12% copper. This means that in every 100 kg of ore, there are 12 kg of copper.

2. **Set Up the Proportion**:
We need to find out how much ore is needed to get 69 kg of copper. We can set up a proportion based on the percentage of copper in the ore.
\[ \text{If } 12 \text{ kg of copper is in } 100 \text{ kg of ore, then } 69 \text{ kg of copper is in } x \text{ kg of ore.} \]
This can be expressed as:
\[ \frac{12 \text{ kg}}{100 \text{ kg}} = \frac{69 \text{ kg}}{x \text{ kg}} \]

3. **Cross-Multiply**:
Cross-multiplying gives us:
\[ 12x = 69 \times 100 \]

4. **Calculate the Right Side**:
Calculate \(69 \times 100\):
\[ 69 \times 100 = 6900 \]
So now we have:
\[ 12x = 6900 \]

5. **Solve for x**:
To find \(x\), divide both sides by 12:
\[ x = \frac{6900}{12} \]

6. **Perform the Division**:
Now calculate \( \frac{6900}{12} \):
\[ x = 575 \]

7. **Conclusion**:
Therefore, the amount of ore required to obtain 69 kg of copper is **575 kg**.

### Final Answer:
575 kg of ore is required to get 69 kg of copper.

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