Assume that y varies inversely as x. If x = 12 when y = 9, what is x when y = -3?

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Assume that y varies inversely as x. If x = 12 when y = 9, what is x when y = -3?

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Answer 1 · 2016-10-04T16:44:14

$x = - 36$ $x = -36$

Explanation:

The basic inverse variation equation is

$x y = k$ $xy = k$

where $k$ $k$ is the constant of variation. In order to write the equation that reflects this relationship, we must find $k$ $k$ . We use the known relationship of $x = 12$ $x = 12$ and $y = 9$ $y = 9$ to find $k$ $k$ . Substituting in the basic equation, we will find $k$ $k$ :

$x y = k$ $xy = k$

$(12) (9) = k$ $(12)(9) = k$

$108 = k$ $108 = k$

This then yields the equation which relates $x$ $x$ and $y$ $y$ :

$x y = 108$ $xy = 108$

Now, use this equation and substitute the second value of $y$ $y$ in order to find its related value of $x$ $x$ :

$x y = 108$ $xy = 108$

$x (- 3) = 108$ $x(-3) = 108$

$x = \frac{108}{- 3}$ $x = 108/(-3)$

$x = - 36$ $x = -36$

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Assume that y varies inversely as x. If x = 12 when y = 9, what is x when y = -3?

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