The ratio of zinc and copper in an alloy is 7:9. If the weight of copper in the alloy is 11.7 kg, find the weight of zinc in it.

Answer

To solve the problem, we will follow these steps:

### Step 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.

### Step 2: Set Up the Relationship
We can express the ratio as a fraction:
\[ \frac{\text{Weight of Zinc}}{\text{Weight of Copper}} = \frac{7}{9} \]

### Step 3: Substitute the Known Value
We know the weight of copper is 11.7 kg. We can substitute this value into the equation:
\[ \frac{\text{Weight of Zinc}}{11.7} = \frac{7}{9} \]

### Step 4: Cross Multiply
To find the weight of zinc, we will cross-multiply:
\[ \text{Weight of Zinc} \times 9 = 7 \times 11.7 \]

### Step 5: Calculate the Right Side
Now, calculate \(7 \times 11.7\):
\[ 7 \times 11.7 = 81.9 \]
So, we have:
\[ \text{Weight of Zinc} \times 9 = 81.9 \]

### Step 6: Solve for Weight of Zinc
Now, divide both sides by 9 to find the weight of zinc:
\[ \text{Weight of Zinc} = \frac{81.9}{9} \]

### Step 7: Perform the Division
Now, calculate \(81.9 \div 9\):
\[ 81.9 \div 9 = 9.1 \]

### Conclusion
Thus, the weight of zinc in the alloy is:
\[ \text{Weight of Zinc} = 9.1 \text{ kg} \]