It x and y vary inversely, fill in the following blanks:

Solution:

(i) Since $x$ and $y$ vary inversely, we have :

$x y=k$

For $x=16$ and $y=6$, we have :

$16 \times 6=k$

$\Rightarrow k=96$

For $x=12$ and $k=96$, we have :

$x y=k$

$\Rightarrow 12 y=96$

$\Rightarrow y=\frac{96}{12}$

$=8$

For $y=4$ and $k=96$, we have :

$x y=k$

$\Rightarrow 4 x=96$

$\Rightarrow x=\frac{96}{4}$

$=24$

For $x=8$ and $k=96$, we have :

$x y=k$

$\Rightarrow 8 y=96$

$\Rightarrow y=\frac{96}{8}$

$=12$

For $y=0.25$ and $k=96$, we have :

$x y=k$

$\Rightarrow 0.25 x=96$

$\Rightarrow x=\frac{96}{0.25}$

$=384$

(ii) Since $x$ and $y$ vary inversely, we have:

$x y=k$

For $x=16$ and $y=4$, we have:

$16 \times 4=k$

$\Rightarrow k=64$

For $x=32$ and $k=64$, we have :

$x y=k$

$\Rightarrow 32 y=64$

$\Rightarrow y=\frac{64}{32}$

$=2$

For $x=8$ and $k=64$

$x y=k$

$\Rightarrow 8 y=64$

$\Rightarrow y=\frac{64}{8}$

$=8$

(iii) Since $x$ and $y$ vary inversely, we have :

$x y=k$

For $x=9$ and $y=27$

$9 \times 27=k$

$\Rightarrow k=243$

For $y=9$ and $k=243$, we have :

$x y=k$

$\Rightarrow 9 x=243$

$\Rightarrow y=\frac{243}{9}$

$=27$

For $x=81$ and $k=243$, we have :

$x y=k$

$\Rightarrow 81 y=243$

$\Rightarrow y=\frac{243}{81}$

$=3$