Beginning Algebra With Applications, Chapter 2, 2.3, Section 2.3, Problem 70

Translate the phrase "the sum of one-eight of a number and one-twelfth of the number" into a variable expression. Then simplify the expression.

$
\begin{equation}
\begin{aligned}
& \text{The unknown number: } n && \text{Assign a variable to one of the number quantities}\\
\\
& \text{One-eight of the number } \frac{1}{8}n && \text{Use the assigned variable to write an expression for any other unknown quantity.}\\
\\
& \text{One-twelfth of the number } \frac{1}{12}n && \text{Again, by using the assigned variable to write an expression for any other unknown quantity.}\\
\\
&= \frac{1}{8}n + \frac{1}{12}n && \text{Use the assigned variable to write the variable expression.}\\
\\
&= \frac{3n + 2n}{24} && \text{Set the LCD}\\
\\
&= \frac{5n}{24} && \text{Simplify}
\end{aligned}
\end{equation}
$