If `x: y = 2 : 3`, then the value of `(3x + 2y)/(x + 5y)` is equal to

Options

A. `12/17`
B. `4/11`
C. `1/2`
D. `5/14`

Answer

To solve the problem where \( x : y = 2 : 3 \) and we need to find the value of \( \frac{3x + 2y}{x + 5y} \), we can follow these steps:

### Step 1: Express \( x \) and \( y \) in terms of a common variable
Since \( x : y = 2 : 3 \), we can express \( x \) and \( y \) as:
\[ x = 2k \quad \text{and} \quad y = 3k \]
where \( k \) is a common multiplier.

### Step 2: Substitute \( x \) and \( y \) into the expression
Now we substitute \( x \) and \( y \) into the expression \( \frac{3x + 2y}{x + 5y} \):
\[ 3x + 2y = 3(2k) + 2(3k) = 6k + 6k = 12k \]
\[ x + 5y = 2k + 5(3k) = 2k + 15k = 17k \]

### Step 3: Write the expression with the substituted values
Now we can write the expression as:
\[ \frac{3x + 2y}{x + 5y} = \frac{12k}{17k} \]

### Step 4: Simplify the expression
Since \( k \) is a common factor in both the numerator and the denominator, we can simplify:
\[ \frac{12k}{17k} = \frac{12}{17} \]

### Final Answer
Thus, the value of \( \frac{3x + 2y}{x + 5y} \) is:
\[ \frac{12}{17} \]

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