Problem of the Week

Updated at Mar 30, 2020 11:07 AM

How would you solve the equation \(5+\frac{2}{5+\frac{5}{t}}=\frac{26}{5}\)?

Below is the solution.



\[5+\frac{2}{5+\frac{5}{t}}=\frac{26}{5}\]

1
Factor out the common term \(5\).
\[5+\frac{2}{5(1+\frac{1}{t})}=\frac{26}{5}\]

2
Subtract \(5\) from both sides.
\[\frac{2}{5(1+\frac{1}{t})}=\frac{26}{5}-5\]

3
Simplify  \(\frac{26}{5}-5\)  to  \(\frac{1}{5}\).
\[\frac{2}{5(1+\frac{1}{t})}=\frac{1}{5}\]

4
Multiply both sides by \(5(1+\frac{1}{t})\).
\[2=\frac{1}{5}\times 5(1+\frac{1}{t})\]

5
Cancel \(5\).
\[2=1+\frac{1}{t}\]

6
Subtract \(1\) from both sides.
\[2-1=\frac{1}{t}\]

7
Simplify  \(2-1\)  to  \(1\).
\[1=\frac{1}{t}\]

8
Multiply both sides by \(t\).
\[t=1\]

Done
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