Question

The number of milligrams of a certain medicine a veterinarian gives a dog varies directly with the weight of the dog. If given a 30 pound dog 3/5 milligrams what is the equation

Answer 1

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

$\bf \stackrel{\textit{\underline{m}illigrams of a certain medicine varies directly with the \underline{w}eight}}{m=kw} \\\\\\ \textit{we also know that } \begin{cases} w=30\\ m=\frac{3}{5} \end{cases}\implies \cfrac{3}{5}=k30\implies \cfrac{3}{5\cdot 30}=k \\\\\\ \cfrac{1}{50}=k\qquad therefore\qquad \boxed{m=\cfrac{1}{50}w}$