Problem of the Week

Updated at Apr 6, 2020 12:22 PM

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Apr 6, 2020

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

Below is the solution.

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

Simplify \(\frac{\frac{v}{5}+5}{5}\) to \(1+\frac{\frac{v}{5}}{5}\).

\[1+\frac{\frac{v}{5}}{5}+2=\frac{77}{25}\]

Simplify \(\frac{\frac{v}{5}}{5}\) to \(\frac{v}{5\times 5}\).

\[1+\frac{v}{5\times 5}+2=\frac{77}{25}\]

Simplify \(5\times 5\) to \(25\).

\[1+\frac{v}{25}+2=\frac{77}{25}\]

Simplify \(1+\frac{v}{25}+2\) to \(\frac{v}{25}+3\).

\[\frac{v}{25}+3=\frac{77}{25}\]

Subtract \(3\) from both sides.

\[\frac{v}{25}=\frac{77}{25}-3\]

Simplify \(\frac{77}{25}-3\) to \(\frac{2}{25}\).

\[\frac{v}{25}=\frac{2}{25}\]

Multiply both sides by \(25\).

\[v=\frac{2}{25}\times 25\]

Cancel \(25\).

\[v=2\]

Done