An alloy contains copper and zinc in the ratio 7 : 3 . If it contains 12 . 6 g of copper, how much does this alloy weight ?

Answer

To solve the problem step by step, we will follow the given information about the alloy containing copper and zinc in the ratio of 7:3.

### Step 1: Understand the Ratio
The ratio of copper to zinc in the alloy is given as 7:3. This means that for every 7 parts of copper, there are 3 parts of zinc.

### Step 2: Define Variables
Let the weight of copper be represented as \( 7x \) and the weight of zinc as \( 3x \). Here, \( x \) is a common multiplier.

### Step 3: Calculate Total Weight of the Alloy
The total weight of the alloy can be expressed as:
\[ \text{Total Weight} = \text{Weight of Copper} + \text{Weight of Zinc} = 7x + 3x = 10x \]

### Step 4: Set Up the Equation
We know that the weight of copper is given as 12.6 grams. Therefore, we can set up the equation:
\[ 7x = 12.6 \]

### Step 5: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 7:
\[ x = \frac{12.6}{7} = 1.8 \]

### Step 6: Calculate the Total Weight of the Alloy
Now that we have the value of \( x \), we can find the total weight of the alloy:
\[ \text{Total Weight} = 10x = 10 \times 1.8 = 18 \text{ grams} \]

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

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