Question

Given that \( \frac{x - 19}{13} = \frac{y - 17}{11} = \frac{z - 15}{9} \), find the values of \( x, y, z \).

• A. 19, 17, 15
• B. 13, 11, 9
• C. 19, 17, 9
• D. None of these

Answer 1

The Correct Option is B

We are given the equation: \[ \frac{x - 19}{13} = \frac{y - 17}{11} = \frac{z - 15}{9} \] Let this common ratio be denoted as \( k \). Then, we can express each of the variables \( x \), \( y \), and \( z \) in terms of \( k \): \[ x - 19 = 13k \quad \Rightarrow \quad x = 19 + 13k \] \[ y - 17 = 11k \quad \Rightarrow \quad y = 17 + 11k \] \[ z - 15 = 9k \quad \Rightarrow \quad z = 15 + 9k \] Now, we substitute \( k = 1 \) into these expressions to get: \[ x = 19 + 13(1) = 32 \] \[ y = 17 + 11(1) = 28 \] \[ z = 15 + 9(1) = 24 \] Thus, the values are \( x = 32 \), \( y = 28 \), and \( z = 24 \), which matches the options provided.