[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \textit{\underline{N} is inversely proportional to \underline{A}}\qquad N=\cfrac{k}{A}
\\\\\\
\textit{we also know that }
\begin{cases}
A=3\\
N=16
\end{cases}\implies 16=\cfrac{k}{3}\implies 16\cdot 3=k
\\\\\\
48=k\qquad thus\qquad \boxed{N=\cfrac{48}{A}}\\\\
-------------------------------\\\\
\textit{if \underline{A} is 4, what is \underline{N}?}\qquad N=\cfrac{48}{4}[/tex]
