Solve Ratio Problem: Find $\frac{x-y}{x+y}$ from $0.02x = 0.5y$
Given the algebraic relationship $0.02x = 0.5y$. The goal is to find the value of the expression $\frac{x-y}{x+y}$.
Step 1: Determine the Ratio $x:y$
Start with the given equation:
$0.02x = 0.5y$To find the ratio $\frac{x}{y}$, divide both sides by $y$ and then by $0.02$:
$\frac{x}{y} = \frac{0.5}{0.02}$Simplify the fraction by multiplying the numerator and denominator by 100:
$\frac{x}{y} = \frac{0.5 \times 100}{0.02 \times 100} = \frac{50}{2} = 25$This shows that $x = 25y$.
Step 2: Substitute Ratio into the Expression
Substitute the value of $x$ (in terms of $y$) into the expression $\frac{x-y}{x+y}$:
$\frac{x-y}{x+y} = \frac{(25y)-y}{(25y)+y}$Combine the terms in the numerator and the denominator:
$\frac{25y - y}{25y + y} = \frac{24y}{26y}$Step 3: Final Simplification
Cancel the common factor $y$ from the numerator and denominator (assuming $y \neq 0$):
$\frac{24}{26}$Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
$\frac{24 \div 2}{26 \div 2} = \frac{12}{13}$Thus, the value of $\frac{x-y}{x+y}$ is $\frac{12}{13}$.
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