# How do you write the equation if Z is inversely proportional to the sum of x and y and the sum of x and y is 10 when Z is 4?

Jun 3, 2015

If $Z$ is inversely proportional to $\left(x + y\right)$
then
$\textcolor{w h i t e}{\text{XXXX}}$$Z \left(x + y\right) = c$ for some constant $c$

If $Z = 4$ and $\left(x + y\right) = 10$ is a solution to this relation
then
$\textcolor{w h i t e}{\text{XXXX}}$$4 \left(10\right) = c \rightarrow c = 40$

and the equation is
$\textcolor{w h i t e}{\text{XXXX}}$$Z \left(x + y\right) = 40$