If `800880 = 8 xx 10^(x) + 8 xx 10^(y) + 8 xx 10^(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 \(800880 = 8 \times 10^{x} + 8 \times 10^{y} + 8 \times 10^{z}\), we will follow these steps:

### Step 1: Understand the Equation
We have the number \(800880\) expressed as a sum of terms involving powers of 10 multiplied by 8. We need to identify the values of \(x\), \(y\), and \(z\) such that the equation holds true.

### Step 2: Rewrite the Number
The number \(800880\) can be broken down into its components:
- The first part is \(800000\) (which is \(8 \times 10^5\)).
- The second part is \(800\) (which is \(8 \times 10^2\)).
- The third part is \(80\) (which is \(8 \times 10^1\)).

### Step 3: Express the Number in Terms of Powers of 10
Now we can express \(800880\) as:
\[ 800880 = 8 \times 10^5 + 8 \times 10^2 + 8 \times 10^1 \]

### Step 4: Identify the Values of \(x\), \(y\), and \(z\)
By comparing the expression \(8 \times 10^{x} + 8 \times 10^{y} + 8 \times 10^{z}\) with our rewritten form, we can identify:
- \(x = 5\)
- \(y = 2\)
- \(z = 1\)

### Step 5: Calculate \(x + y + z\)
Now we can find the sum:
\[ x + y + z = 5 + 2 + 1 = 8 \]

### Final Answer
Thus, the value of \(x + y + z\) is \(8\).

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