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 $A$.