If ` x : y = 3 : 4` then the value of ` ( 5 x - 2y)/( 7 x + 2y)` =

Options

A. `(7)/(25)`
B. `(7)/(23)`
C. `(7)/(29)`
D. `(7)/(17)`

Answer

To solve the problem where \( x : y = 3 : 4 \) and we need to find the value of \( \frac{5x - 2y}{7x + 2y} \), we can follow these steps:

### Step 1: Express \( x \) and \( y \) in terms of a common variable
Given the ratio \( x : y = 3 : 4 \), we can express \( x \) and \( y \) in terms of a variable \( a \):
\[ x = 3a \quad \text{and} \quad y = 4a \]

### Step 2: Substitute \( x \) and \( y \) into the expression
Now, substitute \( x \) and \( y \) into the expression \( \frac{5x - 2y}{7x + 2y} \):
\[ \frac{5(3a) - 2(4a)}{7(3a) + 2(4a)} \]

### Step 3: Simplify the numerator
Calculate the numerator:
\[ 5(3a) - 2(4a) = 15a - 8a = 7a \]

### Step 4: Simplify the denominator
Calculate the denominator:
\[ 7(3a) + 2(4a) = 21a + 8a = 29a \]

### Step 5: Combine the results
Now, we can combine the simplified numerator and denominator:
\[ \frac{7a}{29a} \]

### Step 6: Simplify the fraction
The \( a \) in the numerator and denominator cancels out:
\[ \frac{7}{29} \]

Thus, the value of \( \frac{5x - 2y}{7x + 2y} \) is:
\[ \frac{7}{29} \]

### Final Answer
\(\frac{7}{29}\)

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