The ratio of zinc and copper in an alloy is 7:9. If the weight of copper in the alloy is 12.6 kg, find the weight of zinc in it.

Answer

To solve the problem step by step, we will follow the given information and apply the concept of ratios.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ratio of zinc to copper in the alloy is given as 7:9. This means for every 7 parts of zinc, there are 9 parts of copper.

2. **Identify the Given Information**:
We know the weight of copper in the alloy is 12.6 kg.

3. **Set Up the Proportion**:
We can express the ratio of zinc to copper in terms of their weights:
\[ \frac{\text{Weight of Zinc}}{\text{Weight of Copper}} = \frac{7}{9} \]
Let the weight of zinc be \( z \). Therefore, we can write:
\[ \frac{z}{12.6} = \frac{7}{9} \]

4. **Cross-Multiply to Solve for Zinc**:
Cross-multiplying gives us:
\[ 9z = 7 \times 12.6 \]

5. **Calculate the Right Side**:
Now, calculate \( 7 \times 12.6 \):
\[ 7 \times 12.6 = 88.2 \]
So, we have:
\[ 9z = 88.2 \]

6. **Isolate \( z \)**:
To find \( z \), divide both sides by 9:
\[ z = \frac{88.2}{9} \]

7. **Perform the Division**:
Now, calculate \( \frac{88.2}{9} \):
\[ z = 9.8 \]

8. **Conclusion**:
The weight of zinc in the alloy is 9.8 kg.

### Final Answer:
The weight of zinc in the alloy is **9.8 kg**.