Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 28

Suppose that a cup of low fat milk has 100 calories. The number of calories in a cup of low fat milk is two-thirds the number of calories in a cup of whole milk.

Use this information to write an equation that can be used to find the number of calories in a cup of whole milk: $\underline{n}$ = $\underline{150}$.

If we let $n$ be the number of calories in a cup of whole milk, then $\displaystyle \frac{2}{3} n$ represents the number of calories in a cup of low fat milk, so



$
\begin{equation}
\begin{aligned}

\frac{2}{3} n =& 100
\\
\\
\left( \frac{2}{3} n \right) \left( \frac{3}{2} \right) =& 100 \left( \frac{3}{2} \right)
\\
\\
n =& \frac{300}{2}
\\
\\
n =& 150

\end{aligned}
\end{equation}
$