Problem of the Week

Updated at Sep 10, 2018 3:14 PM

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

How would you solve \(5\times \frac{5}{4\times \frac{5}{z}}=\frac{25}{4}\)?

Check out the solution below!



\[5\times \frac{5}{4\times \frac{5}{z}}=\frac{25}{4}\]

1
Simplify  \(4\times \frac{5}{z}\)  to  \(\frac{20}{z}\).
\[5\times \frac{5}{\frac{20}{z}}=\frac{25}{4}\]

2
Invert and multiply.
\[5\times 5\times \frac{z}{20}=\frac{25}{4}\]

3
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{5\times 5z}{20}=\frac{25}{4}\]

4
Simplify  \(5\times 5z\)  to  \(25z\).
\[\frac{25z}{20}=\frac{25}{4}\]

5
Simplify  \(\frac{25z}{20}\)  to  \(\frac{5z}{4}\).
\[\frac{5z}{4}=\frac{25}{4}\]

6
Multiply both sides by \(4\).
\[5z=\frac{25}{4}\times 4\]

7
Cancel \(4\).
\[5z=25\]

8
Divide both sides by \(5\).
\[z=\frac{25}{5}\]

9
Simplify  \(\frac{25}{5}\)  to  \(5\).
\[z=5\]

Done
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