cellular phone companies. 1. with this plan each person is charged $19.95 per month and $0.31 per minute 2. with this plan each person is charged $40.95 per month and $0.16 per min 3. with this plan each person is charged $80.95 per month with unlimited minutes....define the variable, determine range of airtime for when each plan is least expensive
plan1 = 1995 + 31m
plan2 = 4095 + 16m
plan3 = 8095
investigate the 3 equations,
I let good ol' dependable Wolfram sketch them for you
http://www.wolframalpha.com/input/?i=plot+y+%3D+1995+%2B+31m%2C+y+%3D+4095+%2B+16m%2C+y+%3D+8095
note that the plan3 is just a horizontal straight line
to find the exact intersection points, (there are three), solve them in pairs.
thanks!
To determine the range of airtime for when each plan is least expensive, we need to define a variable and analyze the given information. Let's use the variable "x" to represent the number of minutes of airtime used.
1. Plan 1: With this plan, each person is charged $19.95 per month and $0.31 per minute.
- Total cost = $19.95 + ($0.31 * x)
2. Plan 2: With this plan, each person is charged $40.95 per month and $0.16 per minute.
- Total cost = $40.95 + ($0.16 * x)
3. Plan 3: With this plan, each person is charged $80.95 per month with unlimited minutes.
To determine when each plan is least expensive, we need to compare the total costs of different plans for specific ranges of airtime.
Let's find the break-even point between Plan 1 and Plan 2:
19.95 + 0.31x = 40.95 + 0.16x
0.31x - 0.16x = 40.95 - 19.95
0.15x = 21
x = 21 / 0.15
x = 140
For Plan 1, the total cost would be:
19.95 + (0.31 * 140) = $61.35
For Plan 2, the total cost would be:
40.95 + (0.16 * 140) = $63.95
From this point, Plan 2 becomes more expensive than Plan 1. Thus, we can conclude that Plan 1 is least expensive when airtime (x) is less than 140 minutes.
For Plan 3, as it offers unlimited minutes, the cost remains constant at $80.95 per month, regardless of the airtime used. Therefore, Plan 3 is always least expensive for any range of airtime usage.
In summary, the ranges of airtime for when each plan is least expensive are as follows:
- Plan 1: Airtime less than 140 minutes.
- Plan 2: No range since it becomes more expensive than Plan 1 for all airtime.
- Plan 3: Unlimited minutes, so it is always least expensive.