1/2 of a number is greater than 1/3 of that number by 17. What is the number?

Options

A. 54
B. 84
C. 102
D. 112

Explanation

To solve the problem step by step, we can follow these instructions:

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

### Step 2: Set up the equation
According to the problem, \( \frac{1}{2} \) of the number is greater than \( \frac{1}{3} \) of that number by 17. We can express this mathematically as:
\[ \frac{1}{2}x - \frac{1}{3}x = 17 \]

### Step 3: Find a common denominator
To solve the equation, we need to combine the fractions. The least common multiple (LCM) of 2 and 3 is 6. We will rewrite the fractions with a common denominator:
\[ \frac{3}{6}x - \frac{2}{6}x = 17 \]

### Step 4: Simplify the equation
Now, we can combine the fractions:
\[ \frac{3x - 2x}{6} = 17 \]
This simplifies to:
\[ \frac{x}{6} = 17 \]

### Step 5: Solve for \( x \)
To isolate \( x \), multiply both sides of the equation by 6:
\[ x = 17 \times 6 \]
Calculating this gives:
\[ x = 102 \]

### Conclusion
The number is \( 102 \).

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