# If y=21 when x=-6, how do you find x when y=7 given that y varies inversely as x?

Jul 27, 2017

$x = - 18$

#### Explanation:

$\text{the initial statement is } y \propto \frac{1}{x}$

$\text{to convert to an equation multiply by k the constant}$
$\text{of variation}$

$\Rightarrow y = k \times \frac{1}{x} = \frac{k}{x}$

$\text{to find k use the given condition}$

$y = 21 \text{ when } x = - 6$

$y = \frac{k}{x} \Rightarrow k = y x = 21 \times - 6 = - 126$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = - \frac{126}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when } y = 7$

$x = - \frac{126}{y} = - \frac{126}{7} = - 18$

Jul 27, 2017

$x = - 18$

#### Explanation:

y prop 1/x or y = k*1/x or x*y = k ; k is constant of proportionality.

$y = 21 . x = - 6 \therefore k = x \cdot y = - 6 \cdot 21 = - 126$ .

So the variation equation is  x * y = -126 ; y=7, x = ?

$\therefore x \cdot 7 = - 126 \therefore x = - \frac{126}{7} = - 18$

$x = - 18$ [Ans]