[tex]\bf \qquad \qquad \textit{double proportional variation}\\\\
\begin{array}{llll}
\textit{\underline{y} varies directly with \underline{x}}\\
\textit{and inversely with \underline{z}}
\end{array}\implies y=\cfrac{kx}{z}\impliedby
\begin{array}{llll}
k=constant\ of\\
variation
\end{array}\\\\
-------------------------------\\\\[/tex]
[tex]\bf z=\cfrac{kx}{y}\impliedby
\begin{array}{llll}
\textit{directly proportional to "x"}\\
\textit{and inversely proportional to "y"}
\end{array}
\\\\\\
\textit{we also know that }
\begin{cases}
x=12\\
y=18\\
z=2
\end{cases}\implies 2=\cfrac{k12}{18}\implies \cfrac{2\cdot 18}{12}=k
\\\\\\
\boxed{3=k}\qquad thus\qquad \boxed{z=\cfrac{3x}{y}}\\\\
-------------------------------\\\\
\textit{what's "z" when }
\begin{cases}
x=19\\
y=22
\end{cases}\implies z=\cfrac{3\cdot 19}{22}[/tex]
