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

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Solution

Calculation of the value of $x$ :
For the ratio $x : y$ , the triplicate ratio is $x^{3} : y^{3}$ .
So, the triplicate ratio of $3 : 4$ is $27 : 64$ .
$\Rightarrow 3 x + 1 : 5 x + 3 = 27 : 64 \Rightarrow \frac{3 x + 1}{5 x + 3} = \frac{27}{64} \Rightarrow 64 (3 x + 1) = 27 (5 x + 3) (C r o s s m u l t i p l y i n g b o t h s i d e s) \Rightarrow 192 x + 64 = 135 x + 81 \Rightarrow 192 x - 135 x = 81 - 64 (S e p a r a t i n g t h e v a r i a b l e a n d c o n s t a n t t e r m s) \Rightarrow 57 x = 17 ∴ x = \frac{17}{57} (D i v i d i n g b o t h s i d e s b y 57)$
Final Answer: The value of $x$ is $\frac{17}{57}$ .

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