Three-sevenths of a number is greater than two-fifths of the number by 4. Find the number.

Answer

To solve the problem, we will follow these steps:

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

### Step 2: Set up the equation
According to the problem, three-sevenths of the number is greater than two-fifths of the number by 4. This can be expressed as:
\[ \frac{3}{7}x = \frac{2}{5}x + 4 \]

### Step 3: Eliminate the fractions
To eliminate the fractions, we can find a common denominator. The least common multiple of 7 and 5 is 35. We will multiply every term in the equation by 35:
\[ 35 \cdot \frac{3}{7}x = 35 \cdot \left(\frac{2}{5}x + 4\right) \]

This simplifies to:
\[ 15x = 14x + 140 \]

### Step 4: Rearrange the equation
Now, we will rearrange the equation to isolate \( x \):
\[ 15x - 14x = 140 \]

This simplifies to:
\[ x = 140 \]

### Step 5: State the final answer
The number is \( 140 \).

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