# If y varies inversely as twice x. When x = 4, y = 10. how do you find y when x = 8?

Sep 8, 2017

color(red)(y=5 when $\textcolor{b l u e}{x = 8}$

#### Explanation:

If $y$ varies inversely as twice $x$, then
$\textcolor{w h i t e}{\text{XXX")color(blue)y=color(magenta)c/(2color(green)x)color(white)("xxx}}$for some constant $\textcolor{m a \ge n t a}{c}$

We are told that $\textcolor{g r e e n}{x} = \textcolor{g r e e n}{4}$, $\textcolor{b l u e}{y} = \textcolor{b l u e}{10}$ is a solution to this relation.
so
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{10} = \frac{\textcolor{m a \ge n t a}{c}}{2 \cdot \textcolor{g r e e n}{4}}$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow \textcolor{m a \ge n t a}{c} = 80$

Therefore the relation is
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{y} = \frac{\textcolor{m a \ge n t a}{80}}{2 \textcolor{g r e e n}{x}}$

When $\textcolor{g r e e n}{x} = \textcolor{g r e e n}{8}$, we have
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{y} = \frac{\textcolor{m a \ge n t a}{80}}{2 \cdot \textcolor{g r e e n}{8}} = 5$