how to construct a mathematical model for each plan?

Question

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) 

Answer 1

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!)