Which of the following equations justify the given statement?
"When x is divided by y, the quotient is added to the product of x and y"

Options

A. `x + (y)/(x)`
B. `(y)/(x) + yx`
C. `yx + (2x)/( y)`
D. `(x)/(y) + xy`

Answer

To solve the problem step by step, we need to translate the given statement into a mathematical equation.

### Step-by-Step Solution:

1. **Understand the Statement**: The statement says, "When x is divided by y, the quotient is added to the product of x and y."

2. **Identify the Division**: The first part of the statement involves dividing x by y. In mathematical terms, this is represented as:
\[ \frac{x}{y} \]

3. **Identify the Product**: The second part of the statement mentions the product of x and y. The product is represented as:
\[ xy \]

4. **Combine the Two Parts**: According to the statement, we need to add the quotient (from step 2) to the product (from step 3). This gives us the equation:
\[ \frac{x}{y} + xy \]

5. **Check Against Options**: Now, we need to compare our derived equation with the provided options:
- Option 1: \( x + \frac{y}{x} \)
- Option 2: \( \frac{y}{x} + xy \)
- Option 3: \( yx + \frac{2x}{y} \)
- Option 4: \( \frac{x}{y} + xy \)

Our derived equation matches with **Option 4**:
\[ \frac{x}{y} + xy \]

### Final Answer:
The equation that justifies the given statement is:
\[ \frac{x}{y} + xy \]