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Mathematics

If (3x + 1) : (5x + 3) is the triplicate ratio of 3 : 4, find the value of x.

Ratio Proportion

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Answer

Triplicate ratio of 3 : 4 = 33 : 43 = 27 : 64.

According to question,

(3x + 1) : (5x + 3) = 27 : 64

⇒3x+15x+3=2764⇒64(3x+1)=27(5x+3)⇒192x+64=135x+81⇒192x−135x=81−64⇒57x=17⇒x=1757.\Rightarrow \dfrac{3x + 1}{5x + 3} = \dfrac{27}{64} \\[0.5em] \Rightarrow 64(3x + 1) = 27(5x + 3) \\[0.5em] \Rightarrow 192x + 64 = 135x + 81 \\[0.5em] \Rightarrow 192x - 135x = 81 - 64 \\[0.5em] \Rightarrow 57x = 17 \\[0.5em] \Rightarrow x = \dfrac{17}{57}.

Hence, the value of x is 1757\dfrac{17}{57}.

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