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 u4×5×u−35=−150\frac{u}{4\times 5}\times \frac{u-3}{5}=-\frac{1}{50}?

Here are the steps:



u4×5×u−35=−150\frac{u}{4\times 5}\times \frac{u-3}{5}=-\frac{1}{50}

1
Simplify  4×54\times 5  to  2020.
u20×u−35=−150\frac{u}{20}\times \frac{u-3}{5}=-\frac{1}{50}

2
Use this rule: ab×cd=acbd\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}.
u(u−3)20×5=−150\frac{u(u-3)}{20\times 5}=-\frac{1}{50}

3
Simplify  20×520\times 5  to  100100.
u(u−3)100=−150\frac{u(u-3)}{100}=-\frac{1}{50}

4
Multiply both sides by 100100.
u(u−3)=−2u(u-3)=-2

5
Expand.
u2−3u=−2{u}^{2}-3u=-2

6
Move all terms to one side.
u2−3u+2=0{u}^{2}-3u+2=0

7
Factor u2−3u+2{u}^{2}-3u+2.
(u−2)(u−1)=0(u-2)(u-1)=0

8
Solve for uu.
u=2,1u=2,1

Done
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