Question

If $2x-5:3x+1$ is the duplicate ratio of $2:3$, find the value of $x$.

Answer 1

Calculation of the value of $x$:

For the ratio $x:y$, the duplicate ratio is $x^2:y^2$.

So, the duplicate ratio of $2:3$ is $4:9$.

$$\begin{gathered} \Rightarrow 2x-5:3x+1=4:9 \\ \Rightarrow \frac{2x-5}{3x+1}=\frac{4}{9} \\ \Rightarrow 9(2x-5)=4(3x+1)(Crossmultiplyingbothsides) \\ \Rightarrow 18x-45=12x+4 \\ \Rightarrow 18x-12x=45+4(Separating\mathit{}the\mathit{}variable\mathit{}and\mathit{}constant\mathit{}terms) \\ \Rightarrow 6x=49 \\ \therefore x=\frac{49}{6}(Dividingbothsidesby6) \end{gathered}$$

Final Answer: The value of $x$ is $\frac{49}{6}$.