In an alloy there is 12% of cop per. To get 69 kg of copper, how much alloy will be required?

Options

A. 424kg
B. 575kg
C. 828kg
D. `1736 2/3` kg

Answer

To solve the problem of how much alloy is required to obtain 69 kg of copper when the alloy contains 12% copper, we can follow these steps:

### Step-by-Step Solution:

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

2. **Determine Copper per Gram of Alloy**:
- To find out how much alloy is needed for 1 gram of copper, we can set up a ratio:
\[ \text{Alloy needed for 1 gram of copper} = \frac{100 \text{ grams of alloy}}{12 \text{ grams of copper}} = \frac{100}{12} \text{ grams of alloy} \]

3. **Convert 69 kg to grams**:
- Since we are working with grams, we need to convert 69 kg to grams:
\[ 69 \text{ kg} = 69 \times 1000 \text{ grams} = 69000 \text{ grams} \]

4. **Calculate the Alloy Required for 69 kg of Copper**:
- Now, we can find out how much alloy is needed for 69000 grams of copper:
\[ \text{Alloy needed} = \left(\frac{100}{12}\right) \times 69000 \text{ grams} \]

5. **Perform the Calculation**:
- Calculate the amount of alloy:
\[ \text{Alloy needed} = \frac{100 \times 69000}{12} = \frac{6900000}{12} = 575000 \text{ grams} \]

6. **Convert Grams to Kilograms**:
- Finally, convert the amount of alloy back to kilograms:
\[ \text{Alloy needed in kg} = \frac{575000 \text{ grams}}{1000} = 575 \text{ kg} \]

### Final Answer:
To obtain 69 kg of copper, you will need **575 kg of alloy**.

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