first off, let's convert the decimals to fractions by using a power of 10, because the constant of variation is not a short decimal, so let's do so then,
[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}\\\\
-------------------------------\\\\
P=kQ\qquad \textit{we also know that }
\begin{cases}
Q=31.2\\
\qquad \frac{312}{10}\\
P=20.8\\
\qquad \frac{208}{10}
\end{cases}\implies \cfrac{208}{10}=k\cfrac{312}{10}[/tex]
[tex]\bf \cfrac{\underline{10}}{312}\cdot \cfrac{208}{\underline{10}}=k\implies \cfrac{208}{312}=k\implies \cfrac{2}{3}=k\qquad then\qquad \boxed{P=\cfrac{2}{3}Q}
\\\\\\
\textit{when Q = 15.3, what is \underline{P}?}\quad 15.3\implies \cfrac{153}{10}
\\\\\\
P=\cfrac{2}{3}\cdot \cfrac{153}{10}\implies P=\cfrac{1}{1}\cdot \cfrac{51}{5}\implies P=\cfrac{51}{5}\implies P=10.2[/tex]
