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Mathematics

If (3x - 9) : (5x + 4) is the triplicate ratio of 3 : 4, find the value of x.

Ratio Proportion

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Answer

According to question,

⇒3x−95x+4=3343⇒3x−95x+4=2764⇒64(3x−9)=27(5x+4)⇒192x−576=135x+108⇒192x−135x=108+576⇒57x=684⇒x=12.\Rightarrow \dfrac{3x - 9}{5x + 4} = \dfrac{3^3}{4^3} \\[1em] \Rightarrow \dfrac{3x - 9}{5x + 4} = \dfrac{27}{64} \\[1em] \Rightarrow 64(3x - 9) = 27(5x + 4) \\[1em] \Rightarrow 192x - 576 = 135x + 108 \\[1em] \Rightarrow 192x - 135x = 108 + 576 \\[1em] \Rightarrow 57x = 684 \\[1em] \Rightarrow x = 12.

Hence, x = 12.

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