If x/y = 3/5, then what is the ratio of `(5x+2y)and(5x-2y)`?

Options

A. `5:2`
B. `5:3`
C. `5:8`
D. `3:8`

Answer

To solve the problem, we start with the given ratio \( \frac{x}{y} = \frac{3}{5} \). We need to find the ratio of \( (5x + 2y) \) and \( (5x - 2y) \).

### Step 1: Express x in terms of y
From the ratio \( \frac{x}{y} = \frac{3}{5} \), we can express \( x \) in terms of \( y \):
\[ x = \frac{3}{5}y \]

### Step 2: Substitute x in the expressions
Now, substitute \( x \) in the expressions \( 5x + 2y \) and \( 5x - 2y \):
\[ 5x + 2y = 5\left(\frac{3}{5}y\right) + 2y = 3y + 2y = 5y \]
\[ 5x - 2y = 5\left(\frac{3}{5}y\right) - 2y = 3y - 2y = y \]

### Step 3: Form the ratio
Now, we can form the ratio of \( (5x + 2y) \) to \( (5x - 2y) \):
\[ \text{Ratio} = \frac{5y}{y} \]

### Step 4: Simplify the ratio
Simplifying the ratio, we get:
\[ \text{Ratio} = 5 \]

### Final Answer
Thus, the ratio of \( (5x + 2y) \) to \( (5x - 2y) \) is:
\[ 5 : 1 \]