Question

If \( \frac{x}{y} = 0.45 \), then the value of \[ \frac{3y - x}{3y + x} + \frac{6}{23} \] is:

• A. 0.85
• B. 1.0
• C. 1.95
• D. 2.05

Hint:

Always look for opportunities to simplify terms, like canceling out variables or simplifying fractions.

Answer 1

The Correct Option is B

We are given \( \frac{x}{y} = 0.45 \), which implies \( x = 0.45y \). Substitute \( x = 0.45y \) into the given expression: \[ \frac{3y - 0.45y}{3y + 0.45y} + \frac{6}{23} \] Simplify the fractions: \[ \frac{2.55y}{3.45y} + \frac{6}{23} \] Cancel out \( y \) from the numerator and denominator: \[ \frac{2.55}{3.45} + \frac{6}{23} \] Now simplify \( \frac{2.55}{3.45} \): \[ \frac{2.55}{3.45} = \frac{255}{345} = \frac{17}{23} \] So, the expression becomes: \[ \frac{17}{23} + \frac{6}{23} = \frac{17 + 6}{23} = \frac{23}{23} = 1 \] Thus, the value of the expression is \( 1 \).