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Mathematics

If (3x + 5y) : (3x − 5y) = 7 : 3, find x : y.

Ratio Proportion

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Answer

Given,

(3x + 5y) : (3x − 5y) = 7 : 3,

⇒3x+5y3x−5y=73⇒3(3x+5y)=7(3x−5y)⇒9x+15y=21x−35y⇒15y+35y=21x−9x⇒50y=12x⇒xy=5012⇒xy=256.\Rightarrow \dfrac{3x + 5y}{3x - 5y} = \dfrac{7}{3} \\[1em] \Rightarrow 3(3x + 5y) = 7(3x - 5y) \\[1em] \Rightarrow 9x + 15y = 21x - 35y \\[1em] \Rightarrow 15y + 35y = 21x - 9x \\[1em] \Rightarrow 50y = 12x \\[1em] \Rightarrow \dfrac{x}{y} = \dfrac{50}{12} \\[1em] \Rightarrow \dfrac{x}{y} = \dfrac{25}{6}.

Hence, x : y = 25 : 6.

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