If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is :

Options

A. 2
B. 3
C. 4
D. 6

Answer

To solve the problem, we will follow these steps:

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

2. **Set up the equation**: According to the problem, doubling the number and adding 20 gives the same result as multiplying the number by 8 and subtracting 4. We can express this as an equation:
\[ 2x + 20 = 8x - 4 \]

3. **Rearrange the equation**: To solve for \( x \), we will rearrange the equation to isolate \( x \) on one side. First, let's move all terms involving \( x \) to one side and constant terms to the other side:
\[ 2x + 20 + 4 = 8x \]
Simplifying this gives:
\[ 2x + 24 = 8x \]

4. **Combine like terms**: Now, we will subtract \( 2x \) from both sides of the equation:
\[ 24 = 8x - 2x \]
This simplifies to:
\[ 24 = 6x \]

5. **Solve for \( x \)**: To find \( x \), divide both sides by 6:
\[ x = \frac{24}{6} \]
Simplifying this gives:
\[ x = 4 \]

6. **Conclusion**: The number is \( 4 \).