A number exceeds its 1/9 by 64. What is the number?

Options

A. 90
B. 81
C. 72
D. 180

Answer

To solve the problem, we need to find a number that exceeds its one-ninth by 64. Let's break this down step by step.

### Step 1: Define the variable
Let the number be \( X \).

### Step 2: Set up the equation
According to the problem, the number \( X \) exceeds its one-ninth by 64. This can be expressed mathematically as:
\[ X = \frac{1}{9}X + 64 \]

### Step 3: Rearrange the equation
To isolate \( X \), we can rearrange the equation:
\[ X - \frac{1}{9}X = 64 \]

### Step 4: Combine like terms
To combine the terms on the left side, we can express \( X \) as \( \frac{9}{9}X \):
\[ \frac{9}{9}X - \frac{1}{9}X = 64 \]
\[ \frac{8}{9}X = 64 \]

### Step 5: Solve for \( X \)
Now, we can solve for \( X \) by multiplying both sides by \( \frac{9}{8} \):
\[ X = 64 \times \frac{9}{8} \]

### Step 6: Simplify the expression
Calculating the right side:
\[ X = 64 \times \frac{9}{8} = 64 \div 8 \times 9 = 8 \times 9 = 72 \]

### Conclusion
Thus, the number is \( \boxed{72} \).