If `(3)/(5)` of a number exceeds its `(2)/(7)` by 44, find the number.

Options

A. 120
B. 140
C. 135
D. 145

Answer

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

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

### Step 2: Write the expressions for the fractions
We know that:
- \( \frac{3}{5} \) of the number is \( \frac{3}{5}x \)
- \( \frac{2}{7} \) of the number is \( \frac{2}{7}x \)

### Step 3: Set up the equation
According to the problem, \( \frac{3}{5}x \) exceeds \( \frac{2}{7}x \) by 44. Therefore, we can write the equation:
\[ \frac{3}{5}x - \frac{2}{7}x = 44 \]

### Step 4: Find a common denominator
The common denominator for 5 and 7 is 35. We will convert both fractions:
- \( \frac{3}{5}x = \frac{3 \times 7}{5 \times 7}x = \frac{21}{35}x \)
- \( \frac{2}{7}x = \frac{2 \times 5}{7 \times 5}x = \frac{10}{35}x \)

### Step 5: Substitute back into the equation
Now substituting these back into the equation gives us:
\[ \frac{21}{35}x - \frac{10}{35}x = 44 \]

### Step 6: Simplify the equation
Combine the fractions:
\[ \frac{21x - 10x}{35} = 44 \]
This simplifies to:
\[ \frac{11x}{35} = 44 \]

### Step 7: Solve for \( x \)
To isolate \( x \), multiply both sides by 35:
\[ 11x = 44 \times 35 \]

Now calculate \( 44 \times 35 \):
\[ 44 \times 35 = 1540 \]
So we have:
\[ 11x = 1540 \]

Now divide both sides by 11:
\[ x = \frac{1540}{11} \]

### Step 8: Calculate \( x \)
Now perform the division:
\[ x = 140 \]

### Conclusion
The required number is \( 140 \).

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