Question

Assume that r varies directly with s. If r = 21 when s = 6, find r when s = 12.

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf r=ks\qquad \textit{we also know that } \begin{cases} r=21\\ s=6 \end{cases}\implies 21=k6\implies \cfrac{21}{6}=k \\\\\\ \cfrac{7}{2}=k\qquad therefore\qquad \boxed{r=\cfrac{7}{2}s} \\\\\\ \textit{if s = 12, what is \underline{r}?}\qquad r=\cfrac{7}{2}\cdot 12$