Problem of the Week

Updated at Feb 21, 2022 1:48 PM

This week we have another equation problem:

How can we solve the equation \(\frac{5}{5+\frac{4}{4z}}=\frac{25}{26}\)?

Let's start!



\[\frac{5}{5+\frac{4}{4z}}=\frac{25}{26}\]

1
Cancel \(4\).
\[\frac{5}{5+\frac{1}{z}}=\frac{25}{26}\]

2
Multiply both sides by \(5+\frac{1}{z}\).
\[5=\frac{25}{26}(5+\frac{1}{z})\]

3
Divide both sides by \(25\).
\[\frac{5}{25}=\frac{1}{26}(5+\frac{1}{z})\]

4
Simplify  \(\frac{5}{25}\)  to  \(\frac{1}{5}\).
\[\frac{1}{5}=\frac{1}{26}(5+\frac{1}{z})\]

5
Simplify  \(\frac{5+\frac{1}{z}}{26}\)  to  \(\frac{5}{26}+\frac{\frac{1}{z}}{26}\).
\[\frac{1}{5}=\frac{5}{26}+\frac{\frac{1}{z}}{26}\]

6
Simplify  \(\frac{\frac{1}{z}}{26}\)  to  \(\frac{1}{26z}\).
\[\frac{1}{5}=\frac{5}{26}+\frac{1}{26z}\]

7
Subtract \(\frac{5}{26}\) from both sides.
\[\frac{1}{5}-\frac{5}{26}=\frac{1}{26z}\]

8
Simplify  \(\frac{1}{5}-\frac{5}{26}\)  to  \(\frac{1}{130}\).
\[\frac{1}{130}=\frac{1}{26z}\]

9
Multiply both sides by \(26z\).
\[\frac{1}{130}\times 26z=1\]

10
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{1\times 26z}{130}=1\]

11
Simplify  \(1\times 26z\)  to  \(26z\).
\[\frac{26z}{130}=1\]

12
Simplify  \(\frac{26z}{130}\)  to  \(\frac{z}{5}\).
\[\frac{z}{5}=1\]

13
Multiply both sides by \(5\).
\[z=1\times 5\]

14
Simplify  \(1\times 5\)  to  \(5\).
\[z=5\]

Done
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