If 7676 is divided into four parts proportional to `7:5:3:4` then the smallest part is:

Options

A. 1212
B. 1515
C. 1616
D. 1919

Answer

To solve the problem of dividing 7676 into four parts in the ratio of 7:5:3:4, we can follow these steps:

### Step 1: Understand the Ratio
The given ratio is 7:5:3:4. This means that the total parts of the ratio can be calculated by adding these numbers together.

**Hint:** To find the total number of parts in a ratio, simply add the individual parts together.

### Step 2: Calculate the Total Parts
Add the parts of the ratio:
\[ 7 + 5 + 3 + 4 = 19 \]

### Step 3: Set Up the Equation
Let \( x \) be the common multiplier for the parts of the ratio. The four parts can be expressed as:
- First part: \( 7x \)
- Second part: \( 5x \)
- Third part: \( 3x \)
- Fourth part: \( 4x \)

The total of these parts must equal 7676:
\[ 7x + 5x + 3x + 4x = 7676 \]

### Step 4: Simplify the Equation
Combine the terms:
\[ 19x = 7676 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 19:
\[ x = \frac{7676}{19} \]

### Step 6: Calculate \( x \)
Perform the division:
\[ x = 404 \]

### Step 7: Find the Smallest Part
The smallest part corresponds to the smallest ratio, which is 3. Therefore, we calculate:
\[ \text{Smallest part} = 3x = 3 \times 404 \]

### Step 8: Calculate the Smallest Part
Now, perform the multiplication:
\[ 3 \times 404 = 1212 \]

### Final Answer
Thus, the smallest part is **1212**.

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