Find the value fo x:y, if `(7x - 15y)/(4x + 6y) = (5)/(6).`

Options

A. `60:11`
B. `30:11`
C. `27:13`
D. `17:13`

Explanation

To solve the equation \( \frac{7x - 15y}{4x + 6y} = \frac{5}{6} \) and find the ratio \( x:y \), we can follow these steps:

### Step 1: Cross Multiply
We start by cross-multiplying to eliminate the fraction:

\[ 6(7x - 15y) = 5(4x + 6y) \]

### Step 2: Distribute
Next, we distribute the numbers on both sides:

\[ 42x - 90y = 20x + 30y \]

### Step 3: Rearrange the Equation
Now, we will rearrange the equation to get all terms involving \( x \) on one side and all terms involving \( y \) on the other side:

\[ 42x - 20x = 30y + 90y \]

This simplifies to:

\[ 22x = 120y \]

### Step 4: Solve for the Ratio \( \frac{x}{y} \)
Now, we can express \( \frac{x}{y} \):

\[ \frac{x}{y} = \frac{120}{22} \]

### Step 5: Simplify the Ratio
Next, we simplify \( \frac{120}{22} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:

\[ \frac{x}{y} = \frac{60}{11} \]

### Step 6: Write the Final Ratio
Thus, the ratio \( x:y \) is:

\[ x:y = 60:11 \]

### Final Answer
The value of \( x:y \) is \( 60:11 \).

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