If `(5x+7y):(3x+11y)=2:3`, then find x : y.

Answer

To solve the problem `(5x + 7y) : (3x + 11y) = 2 : 3`, we will follow these steps:

### Step 1: Set up the equation
We can express the ratio as a fraction:
\[ \frac{5x + 7y}{3x + 11y} = \frac{2}{3} \]

### Step 2: Cross multiply
Cross multiplying gives us:
\[ 3(5x + 7y) = 2(3x + 11y) \]

### Step 3: Distribute on both sides
Now, we will distribute the terms:
\[ 15x + 21y = 6x + 22y \]

### Step 4: Rearrange the equation
Next, we will move all terms involving \(x\) to one side and all terms involving \(y\) to the other side:
\[ 15x - 6x = 22y - 21y \]
This simplifies to:
\[ 9x = 1y \]

### Step 5: Express \(x\) in terms of \(y\)
Now we can express \(x\) in terms of \(y\):
\[ x = \frac{1}{9}y \]

### Step 6: Find the ratio \(x : y\)
To find the ratio \(x : y\), we can write:
\[ x : y = \frac{1}{9}y : y \]
This simplifies to:
\[ x : y = 1 : 9 \]

### Final Answer:
Thus, the ratio \(x : y\) is \(1 : 9\).

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