Question

If y varies directly as (x+3) and inversely as (x-3) and y=21 when x=4, what is the equation for y in terms of x?

Answer 1

`\bf \qquad \qquad \textit{double proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\`


`\bf \textit{\underline{y} varies directly as (x+3) and inversely as (x-3)}\implies y=\cfrac{k(x+3)}{x-3} \\\\\\ \textit{we also know that } \begin{cases} y=21\\ x=4 \end{cases}\implies 21=\cfrac{k(4+3)}{4-3}\implies 21=\cfrac{k(7)}{1} \\\\\\ \cfrac{21}{7}=k\implies 3=k\qquad thus\qquad \qquad \boxed{y=\cfrac{3(x+3)}{x-3}}`