Problem of the Week

Updated at Aug 15, 2022 10:29 AM

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

How would you solve \(\frac{20}{y}+4+4y=22\)?

Check out the solution below!



\[\frac{20}{y}+4+4y=22\]

1
Multiply both sides by \(y\).
\[20+4y+4{y}^{2}=22y\]

2
Move all terms to one side.
\[20+4y+4{y}^{2}-22y=0\]

3
Simplify  \(20+4y+4{y}^{2}-22y\)  to  \(20-18y+4{y}^{2}\).
\[20-18y+4{y}^{2}=0\]

4
Factor out the common term \(2\).
\[2(10-9y+2{y}^{2})=0\]

5
Split the second term in \(10-9y+2{y}^{2}\) into two terms.
\[2(2{y}^{2}-4y-5y+10)=0\]

6
Factor out common terms in the first two terms, then in the last two terms.
\[2(2y(y-2)-5(y-2))=0\]

7
Factor out the common term \(y-2\).
\[2(y-2)(2y-5)=0\]

8
Solve for \(y\).
\[y=2,\frac{5}{2}\]

Done

Decimal Form: 2, 2.5
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