If 0.764 y =1.236x, then what is the value of `((y-x)/(y+x))` ?

Options

A. 0.764
B. 0.236
C. 2
D. 0.472

Answer

To solve the equation \(0.764y = 1.236x\) and find the value of \(\frac{y-x}{y+x}\), we can follow these steps:

### Step 1: Express \(y\) in terms of \(x\)
From the equation \(0.764y = 1.236x\), we can isolate \(y\):
\[ y = \frac{1.236}{0.764}x \]

### Step 2: Calculate the ratio \(\frac{y}{x}\)
Now, we can find the ratio \(\frac{y}{x}\):
\[ \frac{y}{x} = \frac{1.236}{0.764} \]

### Step 3: Simplify the ratio
To simplify \(\frac{1.236}{0.764}\), we can multiply both the numerator and denominator by 1000 to eliminate the decimals:
\[ \frac{1.236 \times 1000}{0.764 \times 1000} = \frac{1236}{764} \]

### Step 4: Substitute into the expression \(\frac{y-x}{y+x}\)
Now, we need to find \(\frac{y-x}{y+x}\). We can express this in terms of \(\frac{y}{x}\):
\[ \frac{y-x}{y+x} = \frac{\frac{y}{x} - 1}{\frac{y}{x} + 1} \]

### Step 5: Substitute \(\frac{y}{x}\) into the expression
Substituting \(\frac{y}{x} = \frac{1236}{764}\):
\[ \frac{y-x}{y+x} = \frac{\frac{1236}{764} - 1}{\frac{1236}{764} + 1} \]

### Step 6: Simplify the expression
Now, we simplify the numerator and denominator:
- For the numerator:
\[ \frac{1236}{764} - 1 = \frac{1236 - 764}{764} = \frac{472}{764} \]
- For the denominator:
\[ \frac{1236}{764} + 1 = \frac{1236 + 764}{764} = \frac{2000}{764} \]

### Step 7: Combine the fractions
Now we can combine these:
\[ \frac{y-x}{y+x} = \frac{\frac{472}{764}}{\frac{2000}{764}} = \frac{472}{2000} \]

### Step 8: Simplify the fraction
Now, we can simplify \(\frac{472}{2000}\):
\[ \frac{472 \div 8}{2000 \div 8} = \frac{59}{250} \]

### Final Answer
Thus, the value of \(\frac{y-x}{y+x}\) is:
\[ \frac{59}{250} \]