Problem of the Week

Updated at Apr 6, 2020 12:22 PM

How would you solve the equation \(\frac{\frac{v}{5}+5}{5}+2=\frac{77}{25}\)?

Below is the solution.



\[\frac{\frac{v}{5}+5}{5}+2=\frac{77}{25}\]

1
Simplify  \(\frac{\frac{v}{5}+5}{5}\)  to  \(1+\frac{\frac{v}{5}}{5}\).
\[1+\frac{\frac{v}{5}}{5}+2=\frac{77}{25}\]

2
Simplify  \(\frac{\frac{v}{5}}{5}\)  to  \(\frac{v}{5\times 5}\).
\[1+\frac{v}{5\times 5}+2=\frac{77}{25}\]

3
Simplify  \(5\times 5\)  to  \(25\).
\[1+\frac{v}{25}+2=\frac{77}{25}\]

4
Simplify  \(1+\frac{v}{25}+2\)  to  \(\frac{v}{25}+3\).
\[\frac{v}{25}+3=\frac{77}{25}\]

5
Subtract \(3\) from both sides.
\[\frac{v}{25}=\frac{77}{25}-3\]

6
Simplify  \(\frac{77}{25}-3\)  to  \(\frac{2}{25}\).
\[\frac{v}{25}=\frac{2}{25}\]

7
Multiply both sides by \(25\).
\[v=\frac{2}{25}\times 25\]

8
Cancel \(25\).
\[v=2\]

Done
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