If `4003250 = 4 xx10^(x) + 3xx10^(y) + 2xx10^(z) + 5xx10^(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 break down the number \( 4003250 \) into its components based on powers of ten.

### Step-by-Step Solution:

1. **Express the number in terms of powers of ten:**
- We can rewrite \( 4003250 \) as \( 4 \times 10^6 + 0 \times 10^5 + 0 \times 10^4 + 3 \times 10^3 + 2 \times 10^2 + 5 \times 10^1 + 0 \times 10^0 \).
- This gives us the breakdown:
- \( 4 \) is in the \( 10^6 \) place,
- \( 3 \) is in the \( 10^3 \) place,
- \( 2 \) is in the \( 10^2 \) place,
- \( 5 \) is in the \( 10^1 \) place.

2. **Identify the values of \( x, y, z, w \):**
- From the breakdown, we can assign:
- \( x = 6 \) (from \( 4 \times 10^6 \)),
- \( y = 3 \) (from \( 3 \times 10^3 \)),
- \( z = 2 \) (from \( 2 \times 10^2 \)),
- \( w = 1 \) (from \( 5 \times 10^1 \)).

3. **Calculate \( x + y + z + w \):**
- Now we sum these values:
\[ x + y + z + w = 6 + 3 + 2 + 1 \]
- Performing the addition:
- \( 6 + 3 = 9 \)
- \( 9 + 2 = 11 \)
- \( 11 + 1 = 12 \)

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

### Conclusion:
The final answer is \( 12 \).