If 1.5x=0.04y then what is the value of `(y-x)/(y+x)?`

Answer

To solve the equation \(1.5x = 0.04y\) and find the value of \(\frac{y - x}{y + x}\), we can follow these steps:

### Step 1: Rearranging the given equation
We start with the equation:
\[ 1.5x = 0.04y \]
To make calculations easier, we can express \(1.5\) and \(0.04\) as fractions:
\[ 1.5 = \frac{15}{10} \quad \text{and} \quad 0.04 = \frac{4}{100} \]
Thus, we can rewrite the equation as:
\[ \frac{15}{10}x = \frac{4}{100}y \]

### Step 2: Cross-multiplying
Cross-multiplying gives us:
\[ 15 \cdot 100x = 4 \cdot 10y \]
This simplifies to:
\[ 1500x = 40y \]

### Step 3: Finding the ratio \(\frac{y}{x}\)
Rearranging the equation to find \(\frac{y}{x}\):
\[ \frac{y}{x} = \frac{1500}{40} \]
Simplifying this fraction:
\[ \frac{1500 \div 20}{40 \div 20} = \frac{75}{2} \]
So, we have:
\[ \frac{y}{x} = \frac{75}{2} \]

### Step 4: Expressing \(y - x\) and \(y + x\)
Now we can express \(y - x\) and \(y + x\) in terms of \(x\):
\[ y = \frac{75}{2}x \]
Thus:
\[ y - x = \frac{75}{2}x - x = \left(\frac{75}{2} - 1\right)x = \left(\frac{75}{2} - \frac{2}{2}\right)x = \frac{73}{2}x \]
And:
\[ y + x = \frac{75}{2}x + x = \left(\frac{75}{2} + 1\right)x = \left(\frac{75}{2} + \frac{2}{2}\right)x = \frac{77}{2}x \]

### Step 5: Finding the value of \(\frac{y - x}{y + x}\)
Now we can substitute \(y - x\) and \(y + x\) into the expression:
\[ \frac{y - x}{y + x} = \frac{\frac{73}{2}x}{\frac{77}{2}x} \]
The \(x\) cancels out:
\[ = \frac{73}{77} \]

### Final Answer
Thus, the value of \(\frac{y - x}{y + x}\) is:
\[ \frac{73}{77} \]