If `4003250 = 4 xx 10^(x) + 3 xx 10^(7) + 2 xx 10^(z) + 5 xx 10^(w)`, then `x + y + z + w` is equal to

Options

A. 16
B. 14
C. 12
D. 10

Answer

To solve the equation \( 4003250 = 4 \times 10^{x} + 3 \times 10^{y} + 2 \times 10^{z} + 5 \times 10^{w} \), we will first express the number \( 4003250 \) in terms of powers of 10.

### Step-by-Step Solution:

1. **Write the number in expanded form**:
\[ 4003250 = 4 \times 10^6 + 3 \times 10^3 + 2 \times 10^2 + 5 \times 10^1 \]
- Here, we break down \( 4003250 \) into its components based on the place values.

2. **Identify the coefficients and their corresponding powers of 10**:
- From the expanded form, we can identify:
- The coefficient of \( 10^6 \) is \( 4 \) (which corresponds to \( x \)).
- The coefficient of \( 10^3 \) is \( 3 \) (which corresponds to \( y \)).
- The coefficient of \( 10^2 \) is \( 2 \) (which corresponds to \( z \)).
- The coefficient of \( 10^1 \) is \( 5 \) (which corresponds to \( w \)).

3. **Assign the values to \( x, y, z, w \)**:
- From the above identification:
- \( x = 6 \)
- \( y = 3 \)
- \( z = 2 \)
- \( w = 1 \)

4. **Calculate \( x + y + z + w \)**:
\[ x + y + z + w = 6 + 3 + 2 + 1 = 12 \]

5. **Final answer**:
- Therefore, \( x + y + z + w = 12 \).

### Conclusion:
The value of \( x + y + z + w \) is \( 12 \).