A number exceeds its 1/6 by 30. What is the number ?

Options

A. 120
B. 150
C. 36
D. 24

Answer

To solve the problem "A number exceeds its 1/6 by 30. What is the number?", we will follow these steps:

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

### Step 2: Set up the equation
According to the problem, the number \( X \) exceeds its \( \frac{1}{6} \) by 30. This can be expressed mathematically as:
\[ X = \frac{X}{6} + 30 \]

### Step 3: Eliminate the fraction
To eliminate the fraction, we can multiply the entire equation by 6:
\[ 6X = X + 180 \]
This simplifies to:
\[ 6X - X = 180 \]

### Step 4: Simplify the equation
Now, combine like terms:
\[ 5X = 180 \]

### Step 5: Solve for \( X \)
To find \( X \), divide both sides of the equation by 5:
\[ X = \frac{180}{5} \]
Calculating this gives:
\[ X = 36 \]

### Conclusion
The number is \( 36 \).

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