Suppose z varies directly as x and inversely as the square of y. If x is doubled and y is tripled, what happens to z?
A) $\mathrm { z }$ is one-sixth as large as before
B) $z$ is six times as large as before
C) $\mathrm { z }$ is multiplied by $\frac { 1 } { 18 }$
D) $\mathrm { z }$ is multiplied by $\frac { 2 } { 9 }$

Question

Suppose z varies directly as x and inversely as the square of y. If x is doubled and y is tripled, what happens to z? 
A) $\mathrm { z }$ is one-sixth as large as before
B) $z$ is six times as large as before
C) $\mathrm { z }$ is multiplied by $\frac { 1 } { 18 }$
D) $\mathrm { z }$ is multiplied by $\frac { 2 } { 9 }$

Quizplus · Accepted Answer

Since $z$ varies directly as $x$ and inversely as $y^2$, when $x$ is doubled ($2x$) and $y$ is tripled ($3y$), $z$ becomes $2x/(3y)^2 = 2x/9y^2$, which is $\frac{2}{9}$ times its original value.

Suppose Z Varies Directly as X and Inversely as the Square