If `2 : 9 :: x : 27`, find the value of x.

Options

A. 8
B. 5
C. 6
D. 7

Answer

To solve the proportion \( 2 : 9 :: x : 27 \), we can set it up as a fraction equation:

1. **Set up the equation**:
\[ \frac{2}{9} = \frac{x}{27} \]

2. **Cross-multiply**:
\[ 2 \times 27 = 9 \times x \]

3. **Calculate the left side**:
\[ 54 = 9x \]

4. **Solve for \( x \)**:
To isolate \( x \), divide both sides by 9:
\[ x = \frac{54}{9} \]

5. **Calculate the value of \( x \)**:
\[ x = 6 \]

Thus, the value of \( x \) is \( 6 \).