If 3x+5y3x−5y=73\dfrac{3x + 5y}{3x - 5y} = \dfrac{7}{3}3x−5y3x+5y=37, find x : y.
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Given,
3x+5y3x−5y=73⇒3(3x+5y)=7(3x−5y)⇒9x+15y=21x−35y⇒15y+35y=21x−9x⇒50y=12x⇒x=50y12⇒xy=5012=256⇒x:y=25:6.\dfrac{3x + 5y}{3x - 5y} = \dfrac{7}{3} \\[0.5em] \Rightarrow 3(3x + 5y) = 7(3x - 5y) \\[0.5em] \Rightarrow 9x + 15y = 21x - 35y \\[0.5em] \Rightarrow 15y + 35y = 21x - 9x \\[0.5em] \Rightarrow 50y = 12x \\[0.5em] \Rightarrow x = \dfrac{50y}{12} \\[0.5em] \Rightarrow \dfrac{x}{y} = \dfrac{50}{12} = \dfrac{25}{6} \\[0.5em] \Rightarrow x : y = 25 : 6.3x−5y3x+5y=37⇒3(3x+5y)=7(3x−5y)⇒9x+15y=21x−35y⇒15y+35y=21x−9x⇒50y=12x⇒x=1250y⇒yx=1250=625⇒x:y=25:6.
Hence, the ratio of x : y is 25 : 6.
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