If 3.5X = 0.07 Y, then find the result of [y-x / y + x]
A. 51/49
B. 49/53
C. 49/51
D. 53/57

Options

A. B
B. C
C. D
D. A

Answer

To solve the equation \(3.5X = 0.07Y\) and find the value of \(\frac{Y - X}{Y + X}\), we can follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ 3.5X = 0.07Y \]

### Step 2: Express Y in terms of X
To express \(Y\) in terms of \(X\), we can rearrange the equation:
\[ Y = \frac{3.5}{0.07}X \]

### Step 3: Simplify the fraction
Now, we simplify \(\frac{3.5}{0.07}\):
\[ \frac{3.5}{0.07} = \frac{3.5 \times 100}{7} = \frac{350}{7} = 50 \]
Thus, we have:
\[ Y = 50X \]

### Step 4: Substitute Y into the expression
Now, we substitute \(Y\) into the expression \(\frac{Y - X}{Y + X}\):
\[ \frac{Y - X}{Y + X} = \frac{50X - X}{50X + X} \]

### Step 5: Simplify the expression
This simplifies to:
\[ \frac{49X}{51X} \]

### Step 6: Cancel out X
Assuming \(X \neq 0\), we can cancel \(X\):
\[ \frac{49}{51} \]

### Step 7: Final result
Thus, the result of \(\frac{Y - X}{Y + X}\) is:
\[ \frac{49}{51} \]

### Conclusion
The correct answer is option C: \(\frac{49}{51}\).

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