two-third of a number is greater than one-third of the number by 3. find the number.

Options

A. 7
B. 9
C. 8
D. 6

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript and break it down clearly.

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

### Step 2: Write the equation based on the problem statement
According to the problem, two-thirds of the number is greater than one-third of the number by 3. This can be expressed mathematically as:
\[ \frac{2}{3}x = \frac{1}{3}x + 3 \]

### Step 3: Eliminate the fractions
To eliminate the fractions, we can multiply the entire equation by 3 (the least common multiple of the denominators):
\[ 3 \left( \frac{2}{3}x \right) = 3 \left( \frac{1}{3}x + 3 \right) \]
This simplifies to:
\[ 2x = x + 9 \]

### Step 4: Rearrange the equation
Now, we will rearrange the equation to isolate \( x \). Subtract \( x \) from both sides:
\[ 2x - x = 9 \]
This simplifies to:
\[ x = 9 \]

### Step 5: Conclusion
The number is \( x = 9 \).

### Final Answer
The required number is **9**.

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