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Wizard Mobile offers customers a choice of several monthly plans. The two least expensive ones are Plan A and Plan B. Plan A has no fixed monthly charges, and each minute costs 40 cents. Plan B charges $30 a month, includes 100 free minutes, and each additional minute costs 50 cents.

AFor plan A: write a formula describing the monthly costs as a function of x, the number of

minutes the phone is used.
b) For plan B: write a formula describing the monthly costs as a function of x, the number of
minutes the phone is used.

Verified Answer :

AL2006

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.


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