Problem of the Week

Updated at Jul 13, 2020 3:02 PM

How would you solve \(\frac{\frac{t}{5}+5}{2}+2=\frac{23}{5}\)?

Below is the solution.



\[\frac{\frac{t}{5}+5}{2}+2=\frac{23}{5}\]

1
Simplify  \(\frac{\frac{t}{5}+5}{2}\)  to  \(\frac{\frac{t}{5}}{2}+\frac{5}{2}\).
\[\frac{\frac{t}{5}}{2}+\frac{5}{2}+2=\frac{23}{5}\]

2
Simplify  \(\frac{\frac{t}{5}}{2}\)  to  \(\frac{t}{5\times 2}\).
\[\frac{t}{5\times 2}+\frac{5}{2}+2=\frac{23}{5}\]

3
Simplify  \(5\times 2\)  to  \(10\).
\[\frac{t}{10}+\frac{5}{2}+2=\frac{23}{5}\]

4
Simplify  \(\frac{t}{10}+\frac{5}{2}+2\)  to  \(\frac{t}{10}+\frac{9}{2}\).
\[\frac{t}{10}+\frac{9}{2}=\frac{23}{5}\]

5
Subtract \(\frac{9}{2}\) from both sides.
\[\frac{t}{10}=\frac{23}{5}-\frac{9}{2}\]

6
Simplify  \(\frac{23}{5}-\frac{9}{2}\)  to  \(\frac{1}{10}\).
\[\frac{t}{10}=\frac{1}{10}\]

7
Multiply both sides by \(10\).
\[t=\frac{1}{10}\times 10\]

8
Cancel \(10\).
\[t=1\]

Done
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