If 20 percent of x is 36 less than x percent of x-70, what is the value of x?

Options

A. `140`
B. `120`
C. `100`
D. `50`

Answer

To solve the problem, we need to set up an equation based on the information given.

1. **Understanding the Problem**: We know that 20% of x is 36 less than x% of (x - 70).

2. **Setting Up the Equation**:
- 20% of x can be expressed as \( \frac{20}{100} \times x = \frac{1}{5}x \).
- x% of (x - 70) can be expressed as \( \frac{x}{100} \times (x - 70) = \frac{x(x - 70)}{100} \).
- According to the problem, we have:
\[ \frac{1}{5}x = \frac{x(x - 70)}{100} - 36 \]

3. **Clearing the Fractions**: To eliminate the fractions, we can multiply the entire equation by 100:
\[ 100 \times \frac{1}{5}x = x(x - 70) - 3600 \]
This simplifies to:
\[ 20x = x^2 - 70x - 3600 \]

4. **Rearranging the Equation**: Move all terms to one side:
\[ x^2 - 70x - 20x - 3600 = 0 \]
Combine like terms:
\[ x^2 - 90x - 3600 = 0 \]

5. **Factoring the Quadratic Equation**: We need to factor the quadratic equation:
\[ x^2 - 90x - 3600 = 0 \]
We look for two numbers that multiply to -3600 and add to -90. The numbers -120 and +30 work:
\[ (x - 120)(x + 30) = 0 \]

6. **Finding the Solutions**: Set each factor to zero:
\[ x - 120 = 0 \quad \text{or} \quad x + 30 = 0 \]
This gives us:
\[ x = 120 \quad \text{or} \quad x = -30 \]

7. **Selecting the Valid Solution**: Since x represents a percentage, it cannot be negative. Therefore, the only valid solution is:
\[ x = 120 \]

### Final Answer:
The value of \( x \) is \( 120 \).