If y varies directly with x, if y = 36 when x = -6, how do you find x when y = 54?

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If y varies directly with x, if y = 36 when x = -6, how do you find x when y = 54?

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Answer 1 · 2016-01-16T12:25:03

$x= -9$

Explanation:

Let $k$ be a constant

Breaking down the question into parts:

If $y$ varies directly with $x : -> y=kx........................(1)$
if $y=36$ when $x=-6->36=kxx(-6) ..........(2)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$color(blue)("To find the value of "k)$

Consider equation (1)

$color(brown)(y=kx)$

Divide both sides by $x$ . This is the same as $color(blue)(xx1/x)$

$color(brown)(ycolor(blue)(xx1/x)=kxcolor(blue)(xx1/x))$

$y/x=kxx x/x$

But $x/x=1$ giving:

$k=y/x ........................................(3)$

Substitute values from (2) into equation (3) giving

$color(blue)(k=36/(-6) =-6)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("To find the value of "x" when "y=54)$

Using equation (1)

$y=kx-> 54=-6 x$

$color(blue)(=>x=54/(-6) = -9)$

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If y varies directly with x, if y = 36 when x = -6, how do you find x when y = 54?

1 Answer

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