If ` ( 7 x + 9y)/( 3 x - 4y) = (19)/(8)` then the value of ` (x)/(y)` is

Options

A. `(148)/(1)`
B. ` (1)/( 148)`
C. `(145)/(1)`
D. `(1)/(145)`

Answer

To solve the equation \(\frac{7x + 9y}{3x - 4y} = \frac{19}{8}\) and find the value of \(\frac{x}{y}\), follow these steps:

### Step 1: Cross-Multiply
Start by cross-multiplying to eliminate the fraction:
\[ 8(7x + 9y) = 19(3x - 4y) \]

### Step 2: Distribute
Distribute both sides:
\[ 56x + 72y = 57x - 76y \]

### Step 3: Rearrange the Equation
Rearranging the equation to group all terms involving \(x\) on one side and all terms involving \(y\) on the other side:
\[ 56x - 57x = -76y - 72y \]
This simplifies to:
\[ -x = -148y \]

### Step 4: Solve for \(\frac{x}{y}\)
Dividing both sides by \(-y\):
\[ \frac{x}{y} = 148 \]

Thus, the value of \(\frac{x}{y}\) is \(148\).