Question

If $y$ varies inversely as $x$, and $y=9$ when $x=2$, find $y$ when $x=3$.

Answer 1

From question,
$y\propto x$

$y=\frac{k}{x}$ ------------------(1) [$k$ is proportionality constant]
$xy=k$ ----------------- (2)
This means, for any pairs of $x$ and $y$, the product will be constant.
$x_1{y}_1=x_2{y}_2$ ------- (3)
Method I:
It is given that,
$x_1=2,y_1=9,x_2=3$ and $y_2=?$
On substituting above values in eq (3),
$2\times 9=3\times y_2$
$18=3y_2$
$y_2=\frac{18}{3}=6$

Hence, $y=6$ when $x=3$.

Method II:
We can also evaluate $y$ using the following method.
Given that,
$y=9;x=2$
Lets substitute the $x$ and $y$ values in eq (1) to evaluate $k$,
$9=\frac{k}{2}$
$k=9\times 2$
$k=18$

Again lets substitute $k=18$ and $x=3$ in eq (1) to evaluate $y$,

$y=\frac{18}{3}$

$y=6$
Hence, $y=6$ when $x=3$.