Problem of the Week

Updated at Jul 6, 2026 2:29 PM

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

How would you solve \(\frac{1}{\frac{5}{w}}+\frac{2}{{(\frac{5}{w})}^{2}}=\frac{33}{25}\)?

Check out the solution below!



\[\frac{1}{\frac{5}{w}}+\frac{2}{{(\frac{5}{w})}^{2}}=\frac{33}{25}\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{1}{\frac{5}{w}}+\frac{2}{\frac{{5}^{2}}{{w}^{2}}}=\frac{33}{25}\]

2
Simplify  \({5}^{2}\)  to  \(25\).
\[\frac{1}{\frac{5}{w}}+\frac{2}{\frac{25}{{w}^{2}}}=\frac{33}{25}\]

3
Invert and multiply.
\[\frac{w}{5}+\frac{2}{\frac{25}{{w}^{2}}}=\frac{33}{25}\]

4
Invert and multiply.
\[\frac{w}{5}+2\times \frac{{w}^{2}}{25}=\frac{33}{25}\]

5
Simplify  \(2\times \frac{{w}^{2}}{25}\)  to  \(\frac{2{w}^{2}}{25}\).
\[\frac{w}{5}+\frac{2{w}^{2}}{25}=\frac{33}{25}\]

6
Multiply both sides by \(25\) (the LCM of \(5, 25\)).
\[5w+2{w}^{2}=33\]

7
Move all terms to one side.
\[5w+2{w}^{2}-33=0\]

8
Split the second term in \(5w+2{w}^{2}-33\) into two terms.
\[2{w}^{2}+11w-6w-33=0\]

9
Factor out common terms in the first two terms, then in the last two terms.
\[w(2w+11)-3(2w+11)=0\]

10
Factor out the common term \(2w+11\).
\[(2w+11)(w-3)=0\]

11
Solve for \(w\).
\[w=-\frac{11}{2},3\]

Done

Decimal Form: -5.5, 3
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