Chapter 6.1, Problem 34PPE

(a)

To determine

To find: The number of text message sends or receive in order for the plans to cost the same each month.

Answer to Problem 34PPE

100 text messages send or receive in order for the plans to cost the same each month.

Explanation of Solution

Given information:

Cost of plan: $40

Additional charges of text messages: $0.20

Cost of plan offering unlimited messages: $60

Calculation:

Let the total cost of plan be y and number of text messages be x.

So,

As the cost of plan is $40 and adds $0.20 per messages

  $y=40+0.2x$.........(1)

And the cost of unlimited messages is

  $y=60$........(2)

For getting same cost every month (1)=(2)

  $\begin{array}{l}60=40+0.2x\\ 0.2x=20\\ x=100messages\end{array}$

Conclusion:

100 text message send or receive in order for the plans to cost the same each month.

(b)

To determine

To find: The preferred plan.

Answer to Problem 34PPE

The first plan will be preferred as it is $10 cheaper than the other plan.

Explanation of Solution

Given information:

Cost of plan: $40

Additional charges of text messages: $0.20

Cost of plan offering unlimited messages: $60

Calculation:

In average 50 messages should be text so,

  $\begin{array}{l}y=40+0.2x\\ y=40+0.2(50)\\ y=50\$\end{array}$

The other plan is $60 so first plan is preferred as it is cheaper than the other plan.

Conclusion:

The first plan will be preferred as it is $10 cheaper than the other plan.