If 76 is divided into four parts proportional to 7, 5, 3, 4, then the smallest part is:

Options

A. A) 12
B. B) 15
C. B) 15
D. D) 19

Answer

To solve the problem of dividing 76 into four parts proportional to the numbers 7, 5, 3, and 4, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Ratios**: The parts are to be divided in the ratio of 7:5:3:4.

2. **Calculate the Sum of the Ratios**:
\[ \text{Sum} = 7 + 5 + 3 + 4 = 19 \]

3. **Determine the Value of Each Part**:
Each part can be calculated by taking the total amount (76) and dividing it by the sum of the ratios (19).
\[ \text{Value of one part} = \frac{76}{19} = 4 \]

4. **Calculate Each Part**:
Now, we can find the value of each part by multiplying the value of one part by the respective ratio:
- First part (7 parts):
\[ 7 \times 4 = 28 \]
- Second part (5 parts):
\[ 5 \times 4 = 20 \]
- Third part (3 parts):
\[ 3 \times 4 = 12 \]
- Fourth part (4 parts):
\[ 4 \times 4 = 16 \]

5. **Identify the Smallest Part**:
From the calculated parts (28, 20, 12, 16), the smallest part is:
\[ \text{Smallest part} = 12 \]

### Final Answer:
The smallest part is **12**.

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