When x is subtracted from 2y, the difference is equal to the average of x and y. What is the value of `(x)/(y)`?

Options

A. `(1)/(2)`
B. `(2)/(3)`
C. `1`
D. `(3)/(2)`

Answer

To solve the problem step by step, we will first translate the given information into a mathematical equation, then simplify it to find the ratio of \( \frac{x}{y} \).

### Step 1: Set up the equation
The problem states that when \( x \) is subtracted from \( 2y \), the difference is equal to the average of \( x \) and \( y \).

The average of \( x \) and \( y \) can be expressed as:
\[ \text{Average} = \frac{x + y}{2} \]

So, we can write the equation as:
\[ 2y - x = \frac{x + y}{2} \]

### Step 2: Eliminate the fraction
To eliminate the fraction, we can multiply both sides of the equation by 2:
\[ 2(2y - x) = x + y \]

This simplifies to:
\[ 4y - 2x = x + y \]

### Step 3: Rearrange the equation
Now, we will rearrange the equation to group the \( x \) and \( y \) terms:
\[ 4y - y = x + 2x \]

This simplifies to:
\[ 3y = 3x \]

### Step 4: Solve for the ratio \( \frac{x}{y} \)
Now, we can divide both sides by 3:
\[ y = x \]

Thus, we can express the ratio \( \frac{x}{y} \):
\[ \frac{x}{y} = 1 \]

### Final Answer
The value of \( \frac{x}{y} \) is \( 1 \).

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