Question

The given pair of value form an inverse variation. Find the missing value:
$(3,7),(8,y)$

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 $x=3$ is inversely proportional to $y=7$, therefore,

$xy=k\Rightarrow 3\times 7=k\Rightarrow k=21$

Thus, the general equation is $xy=21$.

Since $x=8$, therefore,

$xy=21\Rightarrow 8y=21\Rightarrow y=\frac{21}{8}=2.62$

Hence, $y=2.62$ when $x=8$.