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If y varies inversely as x, how do you find x when y = 3 if y = 15 when x = 2?

1 Answer

Apr 25, 2016

$x = 10$ $x=10$

Explanation:

If $y$ $y$ varies inversely as $x$ $x$
then
$XXX x \cdot y = c$ $color(white)("XXX")color(blue)(x)*color(red)(y) = color(green)(c)$ for some constant $c$ $c$

We are told when $x = 2$ $color(red)(x=2)$ then $y = 15$ $color(blue)(y=15)$
So
$XXX 2 \cdot 15 = c$ $color(white)("XXX")color(red)(2)*color(blue)(15)=color(green)(c)$

$XXX \Rightarrow c = 30$ $color(white)("XXX")rArr color(green)(c=30)$
and
$XXX x \cdot y = 30$ $color(white)("XXX")color(red)color(red)(x)*color(blue)(y)=color(green)(30)$

Therefore when $y = 3$ $color(blue)(y=3)$
$XXX x \cdot 3 = 30$ $color(white)("XXX")color(red)(x)*color(blue)(3)=color(green)(30)$
$XXX \to x = 10$ $color(white)("XXX")rarr color(red)(x) = 10$

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