If `14/21=x/3=6/y`, then values of x and y are respectively:

Options

A. 2, 9
B. 9, 2
C. 7, 9
D. 2, 7

Answer

To solve the equation \( \frac{14}{21} = \frac{x}{3} = \frac{6}{y} \), we will break it down into two parts to find the values of \( x \) and \( y \).

### Step 1: Solve for \( x \)

We start with the equation:

\[ \frac{14}{21} = \frac{x}{3} \]

To solve for \( x \), we can cross-multiply:

\[ 14 \cdot 3 = 21 \cdot x \]

Calculating the left side:

\[ 42 = 21x \]

Now, divide both sides by 21 to isolate \( x \):

\[ x = \frac{42}{21} = 2 \]

### Step 2: Solve for \( y \)

Next, we take the second part of the equation:

\[ \frac{14}{21} = \frac{6}{y} \]

Again, we cross-multiply:

\[ 14y = 21 \cdot 6 \]

Calculating the right side:

\[ 14y = 126 \]

Now, divide both sides by 14 to isolate \( y \):

\[ y = \frac{126}{14} = 9 \]

### Final Answer

Thus, the values of \( x \) and \( y \) are respectively:

\[ x = 2, \quad y = 9 \]