Question

The given pair of value form an inverse variation. Find the missing value:
$(2.6,4.5),(x,6.3)$

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 $x=2.6$ is inversely proportional to $y=4.5$, therefore,

$xy=k\Rightarrow 2.6\times 4.5=k\Rightarrow k=11.7$

Thus, the general equation is $xy=11.7$.

Since $y=6.3$, therefore,

$xy=11.7\Rightarrow 6.3x=11.7\Rightarrow x=\frac{11.7}{6.3}=1.85$

Hence, $x=1.85$ when $y=6.3$.