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Mathematics

If 5x + 6y : 8x + 5y = 8 : 9, find : x : y.

Ratio Proportion

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Answer

Given,

5x + 6y : 8x + 5y = 8 : 9

5x+6y8x+5y=899(5x+6y)=8(8x+5y)45x+54y=64x+40y64x45x=54y40y19x=14yxy=1419\Rightarrow \dfrac{5x + 6y}{8x + 5y} = \dfrac{8}{9} \\[1em] \Rightarrow 9(5x + 6y) = 8(8x + 5y) \\[1em] \Rightarrow 45x + 54y = 64x + 40y \\[1em] \Rightarrow 64x - 45x = 54y - 40y \\[1em] \Rightarrow 19x = 14y \\[1em] \Rightarrow \dfrac{x}{y} = \dfrac{14}{19}

Hence, x : y = 14 : 19.

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