# If x varies inversely as y and x=12 when y=3, what is the value of x when y=9?

When y=9 ; x=4
$x \propto \frac{1}{y} \mathmr{and} x = k \cdot \frac{1}{y} \mathmr{and} x y = k$ (k is the constant of proportionality)
$x = 12$ when $y = 3 \therefore 12 \cdot 3 = k \mathmr{and} k = 36$.Hence the variation equation is $x y = 36$ when y=9 ; x =36/9=4[Ans]