Question

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

x	12	16	...	8	...
y	...	6	4	...	0.25

 

Answer 1

\[ \text{ Since x and y vary inversely, we have: }  \]
\[xy = k\]
\[\text{ For x = 16 and y = 6, we have: }  \]
\[16 \times 6 = k\]
\[ \Rightarrow k = 96\]
\[\text{ For x = 12 and k = 96, we have } : \]
\[xy = k\]
\[ \Rightarrow 12y = 96\]
\[ \Rightarrow y = \frac{96}{12}\]
\[ = 8\]
\[\text{ For y = 4 and k = 96, we have:}  \]
\[xy = k\]
\[ \Rightarrow 4x = 96\]
\[ \Rightarrow x = \frac{96}{4}\]
\[ = 24\]
\[\text{ For x = 8 and k = 96, we have:}  \]
\[xy = k\]
\[ \Rightarrow 8y = 96\]
\[ \Rightarrow y = \frac{96}{8}\]
\[ = 12\]
\[\text{ For y = 0 . 25 and k = 96, we have:}  \]
\[xy = k\]
\[ \Rightarrow 0 . 25x = 96\]
\[ \Rightarrow x = \frac{96}{0 . 25}\]
\[ = 384\]