Question

P varies directly is Q. When Q = 31.2, P = 20.8. Find P when Q = 15.3.

Answer 1

P = 4.9....................

Answer 2

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,

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ P=kQ\qquad \textit{we also know that } \begin{cases} Q=31.2\\ \qquad \frac{312}{10}\\ P=20.8\\ \qquad \frac{208}{10} \end{cases}\implies \cfrac{208}{10}=k\cfrac{312}{10}$

$\bf \cfrac{\underline{10}}{312}\cdot \cfrac{208}{\underline{10}}=k\implies \cfrac{208}{312}=k\implies \cfrac{2}{3}=k\qquad then\qquad \boxed{P=\cfrac{2}{3}Q} \\\\\\ \textit{when Q = 15.3, what is \underline{P}?}\quad 15.3\implies \cfrac{153}{10} \\\\\\ P=\cfrac{2}{3}\cdot \cfrac{153}{10}\implies P=\cfrac{1}{1}\cdot \cfrac{51}{5}\implies P=\cfrac{51}{5}\implies P=10.2$