Divide 224 into three parts so that the second will be twice the first and third will be twice the second

Options

A. 26,52, 104
B. 24, 48, 96
C. 18, 36, 72
D. 32, 64,128

Answer

To solve the problem of dividing 224 into three parts such that the second part is twice the first part and the third part is twice the second part, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
Let the first part be \( x \).

2. **Express the Other Parts**:
According to the problem:
- The second part is twice the first part, so the second part is \( 2x \).
- The third part is twice the second part, so the third part is \( 2 \times 2x = 4x \).

3. **Set Up the Equation**:
The sum of all three parts must equal 224. Therefore, we can write the equation:
\[ x + 2x + 4x = 224 \]

4. **Combine Like Terms**:
Combine the terms on the left side:
\[ 7x = 224 \]

5. **Solve for \( x \)**:
To find \( x \), divide both sides of the equation by 7:
\[ x = \frac{224}{7} = 32 \]

6. **Find the Three Parts**:
Now that we have \( x \), we can find the three parts:
- First part: \( x = 32 \)
- Second part: \( 2x = 2 \times 32 = 64 \)
- Third part: \( 4x = 4 \times 32 = 128 \)

7. **Conclusion**:
The three parts are:
- First part: 32
- Second part: 64
- Third part: 128

### Final Answer:
The three parts are 32, 64, and 128.

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