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If y varies inversely as x and y = 12 when x = 3, how do you find y when x = 4?

1 Answer

Apr 20, 2016

$y = 9$ $y=9$ when $x = 4$ $x=4$

Explanation:

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

Given $y = 12$ $y=color(red)(12)$ when $x = 3$ $x=color(blue)(3)$
$XXX 3 \cdot 12 = c$ $color(white)("XXX")color(blue)(3) * color(red)(12) = c$

$XXX \Rightarrow c = 36$ $color(white)("XXX")rArr c=36$

So
$XXX x \cdot y = 36$ $color(white)("XXX")x * y = 36$
and when $x = 4$ $x=color(green)(4)$
$XXX 4 \cdot y = 36$ $color(white)("XXX")color(green)(4) * y = 36$

$XXX \Rightarrow y = 9$ $color(white)("XXX")rArr y=9$

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