Problem of the Week

Updated at Mar 8, 2021 3:19 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation \((\frac{u}{5}-5)\times \frac{5}{3-u}=21\)?

Check out the solution below!



\[(\frac{u}{5}-5)\times \frac{5}{3-u}=21\]

1
Expand.
\[\frac{u}{3-u}-\frac{25}{3-u}=21\]

2
Join the denominators.
\[\frac{u-25}{3-u}=21\]

3
Multiply both sides by \(3-u\).
\[u-25=21(3-u)\]

4
Expand.
\[u-25=63-21u\]

5
Add \(25\) to both sides.
\[u=63-21u+25\]

6
Simplify  \(63-21u+25\)  to  \(-21u+88\).
\[u=-21u+88\]

7
Add \(21u\) to both sides.
\[u+21u=88\]

8
Simplify  \(u+21u\)  to  \(22u\).
\[22u=88\]

9
Divide both sides by \(22\).
\[u=\frac{88}{22}\]

10
Simplify  \(\frac{88}{22}\)  to  \(4\).
\[u=4\]

Done
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