If 50% of (x-y) = 30% of (x+y), then what percent of x is y?

Options

A. a. 20%
B. b. 25%
C. c. 30%
D. d. 40%

Answer

To solve the problem, we start with the equation given in the question:

1. **Set up the equation**:
We know that 50% of (x - y) is equal to 30% of (x + y).
This can be written mathematically as:
\[ 0.5(x - y) = 0.3(x + y) \]

2. **Eliminate the decimals**:
To make calculations easier, we can multiply both sides of the equation by 10 to eliminate the decimals:
\[ 5(x - y) = 3(x + y) \]

3. **Expand both sides**:
Now, we expand both sides of the equation:
\[ 5x - 5y = 3x + 3y \]

4. **Rearrange the equation**:
Next, we will rearrange the equation to get all terms involving \(x\) on one side and all terms involving \(y\) on the other side:
\[ 5x - 3x = 3y + 5y \]
This simplifies to:
\[ 2x = 8y \]

5. **Solve for \(y\) in terms of \(x\)**:
Now, we can express \(y\) in terms of \(x\):
\[ y = \frac{2x}{8} = \frac{x}{4} \]

6. **Find the percentage of \(x\) that is \(y\)**:
To find what percent of \(x\) is \(y\), we can set up the following ratio:
\[ \frac{y}{x} \times 100 = \frac{\frac{x}{4}}{x} \times 100 \]
This simplifies to:
\[ \frac{1}{4} \times 100 = 25 \]

Thus, \(y\) is **25% of \(x\)**.