You have been hired by a cell phone company to create two rate plans for customers, one that benefits customers with high usage. The cell phone rates may compare usage of minutes or usage of text messaging. At 500 minutes or 200 text messages, both plans should be within $5 of each other. (There can be multiple answers. I just need the equation.)
we need
|500m - 200t| <= 5
where m and t are the rates in $/minute
To create two rate plans for customers, we can start by assigning variables to represent the usage of minutes and text messages for a given customer. Let's assume the rate per minute is 'm' and the rate per text message is 't'.
For the first rate plan, we will design it to benefit customers with high usage. Let's call it Plan A. In this plan, the equation can be set up as follows:
Plan A Cost = m * 500 + t * x
We are given that when the customer uses 500 minutes or 200 text messages in either plan, both plans should be within $5 of each other. Based on this information, we can calculate the cost of Plan B when the customer uses 500 minutes:
Plan B Cost = m * 500 + t * 500
Now, we can set up an equation to represent the within $5 condition:
Plan A Cost - Plan B Cost ≤ $5
m * 500 + t * x - (m * 500 + t * 500) ≤ $5
Simplifying the equation, we get:
t * x - t * 500 ≤ $5
Now, we can further simplify:
t * (x - 500) ≤ $5
This equation represents the condition where, for any usage of minutes 'x' in Plan A, the difference between the cost of Plan A and Plan B should be within $5.
Keep in mind that you may need additional information or constraints to determine the exact values of 'm' and 't' in order to create the two rate plans.