Question

The given pair of value form an inverse variation. Find the missing value:
$(4,6),(x,3)$

Answer 1

The statement " $y$ varies inversely as $x$ means that when $x$ increases, $y$ decreases by the same factor. In other words, the expression $xy$ is constant:

$xy=k$

where $k$ is the constant of variation.

Here, it is given that $x=4$ is inversely proportional to $y=6$, therefore,

$xy=k\Rightarrow 4\times 6=k\Rightarrow k=24$

Thus, the general equation is $xy=24$.

Since $y=3$, therefore,

$xy=24\Rightarrow 3x=24\Rightarrow x=\frac{24}{3}=8$

Hence, $x=8$ when $y=3$.