Question

If (5x-3y)/(5y-3x)=3/4,the value of x:y is ?

Answer 1

$\frac{5x \frac{x}{y} -3y}{5y-3x}= \frac{3}{4} \\ divide\ both\ numerator\ and\ denominator\ by\ y\\ \\\frac{5 \frac{x}{y} -3 \frac{y}{y} }{5 \frac{y}{y} -3 \frac{x}{y} }= \frac{3}{4}\\ \\\frac{5 \frac{x}{y} -3}{5-3 \frac{x}{y} }= \frac{3}{4}\\ \\take\ \frac{x}{y} =t\\ \\ \frac{5t-3}{5-3t}= \frac{3}{4}\\ \\4(5t-3)=3(5-3t)\\ \\20t-12=15-9t$

$20t+9t=15+12\\ \\29t=27\\ \\t= \frac{27}{29} \\ \\ \frac{x}{y} =\frac{27}{29}\\ \\ \boxed{x:y=27:29}$

Answer 2

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