Problem of the Week

Updated at Sep 16, 2019 4:41 PM

For this week we've brought you this equation problem.

How would you solve \(\frac{u}{4\times 5}\times \frac{u-3}{5}=-\frac{1}{50}\)?

Here are the steps:



\[\frac{u}{4\times 5}\times \frac{u-3}{5}=-\frac{1}{50}\]

1
Simplify  \(4\times 5\)  to  \(20\).
\[\frac{u}{20}\times \frac{u-3}{5}=-\frac{1}{50}\]

2
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{u(u-3)}{20\times 5}=-\frac{1}{50}\]

3
Simplify  \(20\times 5\)  to  \(100\).
\[\frac{u(u-3)}{100}=-\frac{1}{50}\]

4
Multiply both sides by \(100\).
\[u(u-3)=-2\]

5
Expand.
\[{u}^{2}-3u=-2\]

6
Move all terms to one side.
\[{u}^{2}-3u+2=0\]

7
Factor \({u}^{2}-3u+2\).
\[(u-2)(u-1)=0\]

8
Solve for \(u\).
\[u=2,1\]

Done
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