Question

If $x$ varies directly as $y$, and $x=2$ when $y$ is 3 then $x=3$ when $y$ is

• A. $2$
• B. $\frac{2}{3}$
• C. $\frac{9}{2}$
• D. none of these

Answer 1

Answer: (C)

$\frac{9}{2}$

Given, $x$ varies directly as $y$

$\Rightarrow x=ky$ where $k$ is a constant

Now given that, at $x=2,y=3$ putting this in the above equation

$\Rightarrow 2=k\left(3\right)\Rightarrow k=\frac{2}{3}$

Thus our equation becomes $y=\frac{1}{k}x=\frac{3}{2}x$

Hence at $x=3,y=\frac{3}{2}\left(3\right)=\frac{9}{2}$