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how to construct a mathematical model for each plan?

a. A flat fee of $50 per month for unlimited calls (is it 50=x)
 
b. a $30 per month fee for a total of 30 hours of calls and an additional charge of $0.01 per minute for all calls over 30 hours 
 
c. a $5 per month fee and a charge of $0.04 per minute for all calls ( is it 5+.04x)
 
d. a $2 per month fee and a charge of $0.045 per minute for all calls; the fee is waived if the charge for calls is $20 or more
 
e. A charge of $0.05 per minute for all calls; there is no additional fees ( is it .05x) 
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1 Answer

Let y = the monthly phone cost (bill) and x = the number of minutes for all calls
 
a.  y = $50  (y is the cost per month, x is the minutes called, so it's y = 50, not x = 50)
 
b.  The number of minutes over 30 hours (30 hours*60 minutes per hour = 1800 minutes) is = x-1800
 
             |  $30 if x ≤ 1800 minutes
     y = <
             |  $30 + ($.01)(x-1800) if x > 1800 minutes
 
c.   y = $5 + ($0.04)x   (Yes, you got this one right!)
 
 
            |  $2 + ($0.45)x  if  ($0.45)x < $20
d.  y = <
            |  ($0.45)x  if ($0.45)x ≥ 20
 
 
e.  y = ($0.05)x   (Yes, you got this one right as well!)

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thank you! i still do not quite understand (b) the statement is
 
A $30 per month fee for a total of 30 hours of calls and an additional charge of $0.01 per minute for all minutes over 30 hours. 
 
here do i convert the 30 hours into minutes for the equation? and if so how would i do that?
Good catch, Melyssa!  I converted the equation to minutes (30 hours * 60 minutes per hour = 1800 minutes)

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