If $y$ $y$ varies inversely as $x$ $x$ , and $y = 3$ $y = 3$ when $x = 6$ $x = 6$ , what is $x$ $x$ when $y = 18$ $y=18$ ?

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Answer 1 · 2017-04-06T07:16:57

$x = 1$ $x=1$

$y$ $y$ varies inversely as $x$ $x$ means that

$y \propto \frac{1}{x}$ $yprop1/x$

$\Rightarrow y = k \cdot \frac{1}{x} = \frac{k}{x}$ $implies y=k*1/x =k/x$ where $k$ $k$ is some constant.

to find $k$ $k$ , substitute the given values $y = 3$ $y=3$ when $x = 6$ $x=6$

$i . e . 3 = \frac{k}{6} \Rightarrow k = 3 \cdot 6 = 18$ $i.e. 3=k/6 implies k=3*6=18$

$therefore$ the equation becomes:- $y=18/x$ .

Now substituting $y=18$ in this equation;

$18=18/x implies x=18/18 =1$

Hence $x=1$ when $y=18$

If yyy varies inversely as xxx, and y = 3y=3y = 3 when x = 6x=6x = 6, what is xxx when y=18y=18y=18?