Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 56

During one day at an office, one-half of the amount of money in the petty cash drawer was used in the morning, and one-third of the remaining money was used in the afternoon, leaving $\$ 5$ in the petty cash drawer at the end of the day. How much money was in the petty cash drawer at the start of the day?

If we let $x$ be the amount of money at the start of the day, we have


$
\begin{equation}
\begin{aligned}

\frac{1}{2}x + \frac{1}{3} x + 5 =& x
&& \text{Model}
\\
\\
\frac{3(x) + 2(x)}{6} +5 =&x
&& \text{Get the LCD}
\\
\\
\frac{5x}{6} + 5 =& x
&& \text{Add the numerator}
\\
\\
5x + 30 =& 6x
&& \text{Multiply each side by } 6
\\
\\
30 =& x
&& \text{Subtract each side by } 5x


\end{aligned}
\end{equation}
$


Thus, the amount of money was $\$ 30$.