If the numerator of a fraction is increaed y 350 % and the denominator of the fraction is increased by 300% the resultant fraction is `(9)/(22)` . What is the original fraction ?

Options

A. `(3)/(4)`
B. `(5)/(12)`
C. `(7)/(9)`
D. `(4)/(11)`

Explanation

To solve the problem step by step, let's denote the original fraction as \( \frac{x}{y} \).

### Step 1: Understand the changes in the numerator and denominator
- The numerator \( x \) is increased by 350%.
- The denominator \( y \) is increased by 300%.

### Step 2: Calculate the new numerator and denominator
- Increasing the numerator \( x \) by 350% means the new numerator becomes:
\[ x + 3.5x = 4.5x = \frac{450}{100}x \]
- Increasing the denominator \( y \) by 300% means the new denominator becomes:
\[ y + 3y = 4y = \frac{400}{100}y \]

### Step 3: Set up the equation for the resultant fraction
According to the problem, the resultant fraction after these changes is \( \frac{9}{22} \). Therefore, we can set up the equation:
\[ \frac{4.5x}{4y} = \frac{9}{22} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 4.5x \cdot 22 = 9 \cdot 4y \]
This simplifies to:
\[ 99x = 36y \]

### Step 5: Simplify the equation
We can simplify this equation by dividing both sides by 9:
\[ 11x = 4y \]

### Step 6: Express \( y \) in terms of \( x \)
From the equation \( 11x = 4y \), we can express \( y \) in terms of \( x \):
\[ y = \frac{11}{4}x \]

### Step 7: Find the original fraction
The original fraction \( \frac{x}{y} \) can now be expressed as:
\[ \frac{x}{y} = \frac{x}{\frac{11}{4}x} = \frac{4}{11} \]

### Conclusion
Thus, the original fraction is:
\[ \frac{4}{11} \]

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