The ratio between weights of gold and silver in an alloy is `17:3.` If the weight of silver in the alloy is `2.7 g,` find :
the weight of alloy.

Answer

To find the weight of the alloy given the ratio of gold to silver and the weight of silver, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ratio of gold to silver in the alloy is given as 17:3. This means for every 17 parts of gold, there are 3 parts of silver.

2. **Assign Variables**:
Let the weight of silver be represented as \(3x\) and the weight of gold as \(17x\), where \(x\) is a common multiplier.

3. **Set Up the Equation**:
We know from the problem that the weight of silver is \(2.7\) grams. Therefore, we can set up the equation:
\[ 3x = 2.7 \]

4. **Solve for \(x\)**:
To find \(x\), divide both sides of the equation by 3:
\[ x = \frac{2.7}{3} = 0.9 \text{ grams} \]

5. **Calculate the Weight of Gold**:
Now that we have \(x\), we can find the weight of gold:
\[ \text{Weight of gold} = 17x = 17 \times 0.9 = 15.3 \text{ grams} \]

6. **Calculate the Total Weight of the Alloy**:
The weight of the alloy is the sum of the weights of gold and silver:
\[ \text{Weight of alloy} = \text{Weight of gold} + \text{Weight of silver} = 15.3 + 2.7 = 18 \text{ grams} \]

### Final Answer:
The weight of the alloy is **18 grams**.

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