Find the value of 'x' in `x:(3)/(7)::(7)/(9):(5)/(9)`

Options

A. `(4)/(7)`
B. `(3)/(2)`
C. `(3)/(5)`
D. `(9)/(7)`

Answer

To solve the problem \( x : \frac{3}{7} :: \frac{7}{9} : \frac{5}{9} \), we can set up a proportion based on the given ratios.

### Step-by-Step Solution:

1. **Set Up the Proportion:**
The given proportion can be written as:
\[ \frac{x}{\frac{3}{7}} = \frac{\frac{7}{9}}{\frac{5}{9}} \]

2. **Simplify the Right Side:**
To simplify the right side, we can divide \(\frac{7}{9}\) by \(\frac{5}{9}\):
\[ \frac{\frac{7}{9}}{\frac{5}{9}} = \frac{7}{9} \times \frac{9}{5} = \frac{7}{5} \]

3. **Rewrite the Equation:**
Now we can rewrite our equation as:
\[ \frac{x}{\frac{3}{7}} = \frac{7}{5} \]

4. **Cross-Multiply:**
Cross-multiplying gives us:
\[ x \cdot 5 = \frac{3}{7} \cdot 7 \]
Simplifying the right side:
\[ x \cdot 5 = 3 \]

5. **Solve for x:**
Now, divide both sides by 5:
\[ x = \frac{3}{5} \]

### Final Answer:
The value of \( x \) is \( \frac{3}{5} \).