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User:Temperal/Introductory Proportion

< User:Temperal
Revision as of 12:32, 22 September 2007 by Temperal (talk | contribs) (→‎Problem)

Problem

Suppose $\frac{1}{20}$ is either x or y in the following system: \[\begin{cases} xy=\frac{1}{k}\\ x=ky \end{cases}\] Find the possible values of k in terms of x and y.

Solution

Template:Incomplete If $x=\frac{1} {20}$, then $\frac{y} {20} = \frac{1} {k}$ so $ky=20$ or $ky=\frac{1} {20}$. now we get $k=\frac{20} {y}$ and $\frac{1} {20y}$. If $y=\frac{1} {20}$, then we solve again, we get $k=20x$ and $\frac{20} {x}$

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