Question

If y varies directly as x and z, and Y=40 when x=5 and z=4 find y when x=2 and z=1

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 \textit{\underline{y} varies directly as \underline{x} and \underline{z}}\qquad y=kxz \\\\\\ \textit{we also know that } \begin{cases} y=40\\ x=5\\ z=4 \end{cases}\implies 40=k(5)(4)\implies 40=20k \\\\\\ \cfrac{40}{20}=k\implies 2=k\qquad therefore\qquad \boxed{y=2xz} \\\\\\ \textit{now when x = 2 and z = 1, what is \underline{y}?}\qquad y=2(2)(1)`