Question

Suppose that y varies jointly with w and x inversely with z and suppose that y=360 when w=6 x=20 and z=3 write the equation that models the relationship

y= 8wx/z
y=10z/wx
y=10wx/z
y=8z/wx

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 jointly with \underline{w} and \underline{x} inversely with \underline{z}}\qquad y=\cfrac{kwx}{z} \\\\\\ \textit{we also know that } \begin{cases} y=360\\ w=6\\ x=20\\ z=3 \end{cases}\implies 360=\cfrac{k(6)(20)}{3} \\\\\\ \cfrac{360(3)}{(6)(20)}=k\implies 9=k\qquad therefore\qquad \boxed{y=\cfrac{9wx}{z}}`