If `800880=8xx10^(x) + 8 xx 10^(y) + 8 xx10^(z)` where x, y and z are whole numbers, then the value of `x+y+z` is

Options

A. 6
B. 5
C. 11
D. 8

Answer

To solve the equation \( 800880 = 8 \times 10^x + 8 \times 10^y + 8 \times 10^z \) where \( x, y, z \) are whole numbers, we can follow these steps:

### Step 1: Express the number in terms of powers of 10
We start by rewriting the number \( 800880 \) in a way that highlights its components related to powers of 10. We can break it down as follows:
\[ 800880 = 800000 + 800 + 0 \]
This can be expressed in terms of powers of 10:
\[ 800000 = 8 \times 10^5 \]
\[ 800 = 8 \times 10^2 \]
\[ 0 = 0 \times 10^n \quad (\text{for any } n) \]

### Step 2: Combine the components
Now we can combine these components:
\[ 800880 = 8 \times 10^5 + 8 \times 10^2 + 8 \times 10^0 \]
However, since we are only interested in \( x, y, z \) being whole numbers, we can ignore the term with \( 0 \) as it does not contribute to the sum.

### Step 3: Identify the values of \( x, y, z \)
From our expression, we can see:
- The term \( 8 \times 10^5 \) corresponds to \( x = 5 \)
- The term \( 8 \times 10^2 \) corresponds to \( y = 2 \)
- The term \( 8 \times 10^0 \) corresponds to \( z = 0 \)

### Step 4: Calculate \( x + y + z \)
Now we can calculate the sum:
\[ x + y + z = 5 + 2 + 0 = 7 \]

### Final Answer
Thus, the value of \( x + y + z \) is \( 7 \).

---