If a number `6573547 times 45` is divisible by 9, then find the value of x.

Options

A. 7
B. 0
C. 8
D. 6

Answer

To solve the problem, we need to determine the value of \( x \) such that the number \( 6573547x45 \) is divisible by 9. According to the divisibility rule for 9, a number is divisible by 9 if the sum of its digits is divisible by 9.

### Step-by-Step Solution:

1. **Identify the digits of the number**: The number is \( 6573547x45 \). The digits are \( 6, 5, 7, 3, 5, 4, 7, x, 4, 5 \).

2. **Calculate the sum of the known digits**:
\[ 6 + 5 + 7 + 3 + 5 + 4 + 7 + 4 + 5 = 46 \]

3. **Include \( x \) in the sum**: The total sum of the digits will be:
\[ 46 + x \]

4. **Determine the condition for divisibility by 9**: We need \( 46 + x \) to be divisible by 9.

5. **Find the smallest multiple of 9 greater than 46**: The multiples of 9 are \( 0, 9, 18, 27, 36, 45, 54, 63, \ldots \). The smallest multiple of 9 that is greater than 46 is 54.

6. **Set up the equation**: We need to solve for \( x \):
\[ 46 + x = 54 \]

7. **Solve for \( x \)**:
\[ x = 54 - 46 = 8 \]

8. **Conclusion**: The value of \( x \) is \( 8 \).

### Final Answer:
The value of \( x \) is \( 8 \).