If `(x+2y)/(y)=5`, what is the value of `(y)/(x)` ?

Options

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

Explanation

To solve the equation \(\frac{x + 2y}{y} = 5\) and find the value of \(\frac{y}{x}\), we can follow these steps:

### Step 1: Start with the given equation
\[ \frac{x + 2y}{y} = 5 \]

### Step 2: Multiply both sides by \(y\) to eliminate the fraction
\[ x + 2y = 5y \]

### Step 3: Rearrange the equation to isolate \(x\)
Subtract \(2y\) from both sides:
\[ x = 5y - 2y \]
This simplifies to:
\[ x = 3y \]

### Step 4: Find \(\frac{y}{x}\)
Now that we have \(x\) in terms of \(y\), we can express \(\frac{y}{x}\):
\[ \frac{y}{x} = \frac{y}{3y} \]

### Step 5: Simplify the fraction
\[ \frac{y}{x} = \frac{1}{3} \]

### Final Answer
Thus, the value of \(\frac{y}{x}\) is \(\frac{1}{3}\).

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