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 (u5−5)×53−u=21(\frac{u}{5}-5)\times \frac{5}{3-u}=21?

Check out the solution below!



(u5−5)×53−u=21(\frac{u}{5}-5)\times \frac{5}{3-u}=21

1
Expand.
u3−u−253−u=21\frac{u}{3-u}-\frac{25}{3-u}=21

2
Join the denominators.
u−253−u=21\frac{u-25}{3-u}=21

3
Multiply both sides by 3−u3-u.
u−25=21(3−u)u-25=21(3-u)

4
Expand.
u−25=63−21uu-25=63-21u

5
Add 2525 to both sides.
u=63−21u+25u=63-21u+25

6
Simplify  63−21u+2563-21u+25  to  −21u+88-21u+88.
u=−21u+88u=-21u+88

7
Add 21u21u to both sides.
u+21u=88u+21u=88

8
Simplify  u+21uu+21u  to  22u22u.
22u=8822u=88

9
Divide both sides by 2222.
u=8822u=\frac{88}{22}

10
Simplify  8822\frac{88}{22}  to  44.
u=4u=4

Done
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