Abc Telecom

Fred has been a customer of ABC Telecom, his local cell phone company, for a year and his plan is about to expire. ABC Telecom has some new plans that Fred is interested in; an unlimited plan for $49.95, or a plan with 500 minutes per month with an overage charge of $0.025 per minute for $24.95. Over the last year, Fred estimates he uses about 750 minutes per month and needs to find the most inexpensive option for the next year. Determine which plan is the most advantageous based on Fred's monthly calling needs.

In order to solve this equation, we need to break down the price plans into individual equations. We will

call the unlimited plan, Plan U, and the 500 minute plan, Plan M. Here is the breakdown of the cost for

each plan:

Plan M: 500 minutes for $24.95 with each additional minute at $0.025

Plan U: Unlimited minutes for $49.95

Let x = # of minutes and y = cost of talking x minutes

Equation for Plan M: y = 24.95 + 0.025 * (x - 500) with (x > 500)

Equation for Plan U: y = 49.95

Plan U has a fixed cost of $49.95 for an infinite number of minutes. Plan M has a fixed cost of $24.95 for a fixed number of minutes (500 minutes), however Fred will need to pay $0.025 per minute over 500 minutes. So when x = # of minutes on Plan M, these amounts are multiplied by the number of minutes above 500 minutes.

Fred has to solve:

Plan M: y = 24.95 + 0.025 (x - 500)

Plan U: y = 49.95

Substituting a value of y from the first equation to the second, we get:

24.95 + 0.025 (x - 500) = 49.95

24.95 + 0.025x - 12.5 = 49.95

0.025x + 12.45 = 49.95

0.025x = 37.50

x = 37.50 / 0.025

x = 1500

When the number of minutes = 1500, the cost of the plans is the same in both plans.

And the cost is:

y = 24.95 + 0.025 (1500 - 500)

y = 24.95 + 0.025 * 1000

y = 24.95 + 25

y = $49.95

When the number of minutes is less than 1500 minutes, Plan M is better.

When the number of minutes is greater than 1500 minutes, Plan U is better.

As Fred