An alloy of zinc and copper weights `13(1)/(2) kg.` If the ratio fo zinc to copper is `2:3` in the alloy, find the weight of copper in the alloy in grams.

Answer

To solve the problem step by step, we will follow the given information about the alloy of zinc and copper.

### Step-by-Step Solution:

1. **Convert the total weight of the alloy into a fraction:**
The total weight of the alloy is given as \( 13 \frac{1}{2} \) kg.
To convert this into an improper fraction:
\[ 13 \frac{1}{2} = 13 + \frac{1}{2} = \frac{26}{2} + \frac{1}{2} = \frac{27}{2} \text{ kg} \]

**Hint:** To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator.

2. **Set up the ratio of zinc to copper:**
The ratio of zinc to copper is given as \( 2:3 \). This means for every 2 parts of zinc, there are 3 parts of copper.

3. **Define the variable for the parts:**
Let \( x \) be the common factor for the ratio. Therefore:
- Weight of zinc = \( 2x \)
- Weight of copper = \( 3x \)

4. **Write the equation for the total weight:**
The total weight of the alloy is the sum of the weights of zinc and copper:
\[ 2x + 3x = 5x \]
Since the total weight of the alloy is \( \frac{27}{2} \) kg, we can set up the equation:
\[ 5x = \frac{27}{2} \]

5. **Solve for \( x \):**
To find \( x \), divide both sides by 5:
\[ x = \frac{27}{2} \div 5 = \frac{27}{2} \times \frac{1}{5} = \frac{27}{10} = 2.7 \text{ kg} \]

**Hint:** When dividing fractions, multiply by the reciprocal of the divisor.

6. **Calculate the weight of copper:**
The weight of copper is given by \( 3x \):
\[ \text{Weight of copper} = 3 \times 2.7 = 8.1 \text{ kg} \]

7. **Convert the weight of copper to grams:**
Since 1 kg = 1000 grams, we convert the weight of copper to grams:
\[ 8.1 \text{ kg} = 8.1 \times 1000 = 8100 \text{ grams} \]

### Final Answer:
The weight of copper in the alloy is **8100 grams**.