Chapter 3.3, Problem 18P

You wonder if you can save money by using your cell phone for all long distance calls. Long distance calls cost $ .05 per minute on your cell phone. The basic plan for your cell phone is $ 29.99 each month. The cost of regular phone service with unlimited long distance is $ 39.99. Define a variable and write an inequality that will help you find the number of long-distance call minutes you may make and still save money.

To determine

The number of long-distance call minutes, an inequality and also define a variable.

Answer to Problem 18P

The number of long distance call minutes are 200.

Inequality is given below;

  $29.99+0.05x\le 39.99$ .

  $x$ variable is number of minutes of long-distance call.

Explanation of Solution

Given:

Long distance call cost $0.05 per minute.

The basic plan is $29.99.

Cost of regular phone services with unlimited long distance is $39.9.

Let number of long-distance call minute is x.

So, for x minutes, total cost per months:

  $=\$29.99\left(\text{basic charge}\right)+\$\left(x\times 0.05\right)\left(\text{call cost}\right)$

Since, unlimited long-distance plan price = $39.99.

For being in profit (to save money with basic plan):

  $\begin{array}{l}\$\left[29.99+\left(x\times 0.005\right)\right]\le \$39.99\\ 29.99+0.05x\le \$39.99\\ x\le \$200\end{array}$

Hence, x is number of minutes of long-distance call.