Wizard Mobile offers customers a choice of several monthly plans. The two least expensive ones are Plan A and Plan B.
- Plan A: No fixed monthly charges; each minute costs 40 cents.
- Plan B: $30 monthly charge, includes 100 free minutes; each additional minute costs 50 cents.
a) For Plan A, write a formula describing the monthly cost as a function of [tex]x[/tex], the number of minutes the phone is used.
b) For Plan B, write a formula describing the monthly cost as a function of [tex]x[/tex], the number of minutes the phone is used.
Answer (2)
x = the number of minutes the phone is used
Plan A: 40¢ per minute ($0.40) no other costs Cost for 1 month = 0.4 x
Plan B: $30 a month, even if you don't use the phone at all 100 free minutes then 50¢ per minute ($0.50)
Cost for 1 month:
If 'x' is less than 100: Cost = 30
If 'x' is greater than 100 :
Cost = 30 + 0.5(x - 100) (Because the first 100 minutes are free, and you only pay for minutes past 100. There are [x-100] of those.)
Eliminate parentheses: Cost = 30 + 0.5x - 50
Combine like terms: *** Cost = 0.5x - 20***
Which plan costs more ? It depends on how many minutes you use in a month. If you use a small number of minutes, Plan A costs you more. If you use a huge number of minutes, Plan B costs you more.
Where is the crossover point ? It's the number of minutes in one month where the costs of both plans are equal.
If you use the phone for less than 100 minutes a month, (where the cost of Plan B starts increasing with each minute):
0.4x = 30
Divide each side by 0.4: x = 75
Less than 75 minutes per month, Plan A costs less. Past 75 minutes a month, Plan A costs more than $30, so Plan B costs less, until Plan B starts charging for extra minutes.
If you use the phone for more than 100 minutes a month:
0.4 x = 0.5 x - 20
Add 20 to each side: 0.4 x + 20 = 0.5 x
Subtract 0.4x from each side: 20 = 0.1 x
Multiply each side by 10: *** 200 = x***
There it is.
Now we can combine the results:
-- Less than 75 minutes in a month: Plan A costs less.
-- Between 75-200 minutes in a month: Plan B costs less.
-- More than 200 minutes a month: Plan A costs less again.
Complicated ? Absolutely ! That's why citizens' consumer groups are after these companies, to try to get them to make their plans more understandable to regular people. I know from personal experience that even a lot of the salesmen in the phone stores could not figure this out and give you sound advice.
The formulas for the monthly costs are: Plan A: C os t = 0.40 x where x is minutes used. For Plan B: C os t = 30 if x ≤ 100 and C os t = 0.50 x − 20 if 100"> x > 100 . This demonstrates how both plans charge differently based on usage.
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