Question

Determine the equation of the joint value

Answer 1

$\bf \qquad \textit{direct proportional variation}\\\\ \begin{array}{cccccclllll} \textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\ \textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\ y&=&{{ k}}&\cdot&x \\ && y={{ k }}x \end{array}\\\\ -----------------------------$

$\bf \textit{x varies directly with y and z}\implies x=\underline{k}yz\qquad \underline{k}= \begin{array}{llll} constant\ of\\ variation \end{array} \\\\\\ \textit{we also know that } \begin{cases} x=120\\ y=5\\ z=8 \end{cases}\implies 120=k(5)(8)\implies \cfrac{120}{5\cdot 8}=k \\\\\\ \boxed{3=k}\qquad thus\implies x=\underline{3}yz \\\\\\ \textit{now what's "x" when } \begin{cases} y=6\\ z=2 \end{cases}\implies x=3(6)(2)$