Mr. Keskin and his wife have a cell phone plan that charges them $5 for 200 text messages per month for each of their phones. The Keskins are charged an additional $0.12 for each text message over their 200-text-message limit. Their carrier has offered them unlimited text messages for both lines for $30. What is the maximum number of text messages that they can send in a month to keep their current plan as the better deal? What is the minimum?

Question

Mr. Keskin and his wife have a cell phone plan that charges them $5 for 200 text messages per month for each of their phones. The Keskins are charged an additional $0.12 for each text message over their 200-text-message limit. Their carrier has offered them unlimited text messages for both lines for $30. What is the maximum number of text messages that they can send in a month to keep their current plan as the better deal? What is the minimum?

Answer 1

2(5+.12(m-200)) < 30

minimum? 0 of course.

Answer 2

To determine the maximum number of text messages the Keskins can send in a month to keep their current plan as the better deal, we need to compare the cost of their current plan with the cost of the unlimited text messages plan.

First, let's calculate the cost of their current plan if they go over their 200-text-message limit:

Additional text messages over the limit = Total text messages - 200
Additional cost for text messages = Additional text messages x $0.12

Total cost of current plan = $5 (base cost) + Additional cost for text messages

Now, let's calculate the cost of the unlimited text messages plan:

Total cost of unlimited plan = $30 (flat fee for both lines)

To determine the maximum number of text messages, we need to find the point at which the cost of the current plan exceeds the cost of the unlimited plan.

Setting the two costs equal to each other:

$5 + Additional cost for text messages = $30

Simplifying the equation:

Additional cost for text messages = $30 - $5
Additional cost for text messages = $25

Now, let's calculate the maximum number of text messages that would result in an additional cost of $25:

Additional text messages x $0.12 = $25
Additional text messages = $25 / $0.12

Using the above calculation, we can determine the maximum additional text messages the Keskins can send. This number represents the point at which the unlimited plan becomes a better deal than their current plan.

To calculate the minimum number of text messages, we need to determine the point at which the cost of the current plan is still cheaper than the unlimited plan.

Setting the two costs equal to each other:

$5 + Additional cost for text messages = $30

Simplifying the equation:

Additional cost for text messages = $30 - $5
Additional cost for text messages = $25

So, the minimum number of text messages they can send and still have their current plan as the better deal is 0. Any number of text messages below the maximum calculated above would result in a cost lower than $25.