[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------[/tex]
[tex]\bf \textit{\underline{V} varies jointly with \underline{B} and \underline{h}}\qquad V=kBh
\\\\\\
\textit{we also know that }
\begin{cases}
B=27\\
h=6\\
V=54
\end{cases}\implies 54=k(27)(6)\implies \cfrac{54}{(27)(6)}=k
\\\\\\
\cfrac{1}{3}=k\qquad therefore\qquad \boxed{V=\cfrac{1}{3}Bh}
\\\\\\
\textit{when h = 12, and V = 124, what is \underline{B}?}\qquad 124=\cfrac{1}{3}B(12)[/tex]
