College Algebra, Chapter 1, 1.6, Section 1.6, Problem 84

Suppose that a telephone company offers two long distance plans $A$ and $B$. The monthly charges for $A$ and $B$ are \$25 and \$5 respectively. While the charges per minute for $A$ is 5 cents per minute, while $B$ is 12 cents per minute.
For how many minutes of long distance calls would plan $B$ be financially advantageous?

If we let $x$ be the duration of long-distance calls in minutes and if $B$ is cheapter, then...

$
\begin{equation}
\begin{aligned}
B & < A \\
\\
5 + \frac{5}{100} x & < 25 + \frac{5}{100} x && \text{model, recall that } \$1 = 100 \text{cents}\\
\\
\frac{12}{100} x - \frac{5}{100} x & < 25 - 5 && \text{Subtract } \frac{5}{100}x \text{ and } 5\\
\\
\frac{7x}{100} & < 20 && \text{Multiply both sides by } \frac{100}{7}\\
\\
x & < \frac{100}{7} (20)\\
\\
x & < \frac{2000}{7}
\end{aligned}
\end{equation}
$


It shows that the duration of call is less than $\displaystyle \frac{2000}{7} \text{min}$, Plan $B$ will be cheapter than Plan $A$.