Question

If x varies directly with y and x=3.5 when y=14 find x when y=18

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{x} varies directly with \underline{y}}\qquad \qquad x=ky\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} x=3.5\\ y=14 \end{cases}\implies 3.5=k14\implies \cfrac{3.5}{14}=k \\\\\\ \cfrac{1}{4}=k\qquad therefore\qquad \boxed{x=\cfrac{1}{4}y} \\\\\\ \textit{when y = 18, what is \underline{x}?}\qquad x=\cfrac{1}{4}(18)$