If \(p\) is inversely proportional to \(q\), and \(p=4\) when \(q=7\):
Find \(p\) when \(q=9\)
\begin{align}p & \propto \frac{1}{q}\\
So \quad p & =k (\frac{1}{q}) \\
By \; substitution \quad 4 & =k(\frac{1}{7})\\
k & =28\\
\therefore \quad p & = 28(\frac{1}{q})\\
And \; when \; q & =9\\
p & = 28(\frac{1}{9})\\
\therefore \quad p & =\frac{28}{9}
\end{align}
Find \(q\) when \(p=3\)
\begin{align}p & \propto \frac{1}{q}\\
So \quad p & =k (\frac{1}{q}) \\
By \; substitution \quad 4 & =k(\frac{1}{7})\\
k & =28\\
\therefore \quad p & = 28(\frac{1}{q})\\
And \; when \; p & =3\\
3 & = 28(\frac{1}{q})\\
\therefore \quad q & =\frac{28}{3}
\end{align}