Chapter 2.3, Problem 11OE

To determine

The minutes to use the telephone each month to make Plan A the better option.

Answer to Problem 11OE

  $160\text{min}$

Explanation of Solution

Given:

The given terms are:

Cost of Plan A=$18.50

Cost of Plan B=$6.50+0.10(x+40)

Calculation:

The solution for the given statement can be obtained by:

Let the number of minutes=x

Cost of Plan A=$18.50

Cost of Plan B=$6.50+0.10(x+40)

Plan A= Plan B

  $\begin{array}{l}\text{18}\text{.50=6}\text{.5+0}\text{.10(x-40)}\\ \text{18}\text{.5=6}\text{.5+0}\text{.10x-4}\\ \text{12=0}\text{.10x-4}\\ \text{x=160}\end{array}$

So, this says that after the plans cost the same ($18.50) per month with both using 160 minutes.

Now let x =161

And solve the right side

  $\begin{array}{l}\text{6}\text{.5+0}\text{.1(161-40)}\\ \text{6}\text{.5+16}\text{.1-4}\\ \text{18}\text{.6}\end{array}$

So, at 161 minutes, Plan B becomes more expensive than Plan A ( Plan B costs $18.60).

Therefore, Plan A is cheaper.