Question

If $x$ varies as $y$ and if $x=6$ when $y=3$, find $x$ when $y$ when $y=10$

Answer 1

The statement " $x$ varies directly as $y$ ," means that when $y$ increases, $x$ increases by the same factor. In other words, $y$ and $x$ always have the same ratio that is:

$x=ky$

where $k$ is the constant of variation.

Here, it is given that $x$ varies as $y$, if $x=6$ and $y=3$, therefore,

$x=ky\Rightarrow 6=k\times 3\Rightarrow 6=3k\Rightarrow k=\frac{6}{3}=2$

Thus, the general equation is $x=2y$.

Since $y=10$, therefore,

$x=2\times 10=20$

Hence, $x=20$ when $y=10$.