Question 1138733: The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for
31
minutes of calls is
$18.31
and the monthly cost for
87
minutes is
$25.03
. What is the monthly cost for
86
minutes of calls?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the monthly cost for 31 minutes is $18.31.
if there were no fixed monthly charges, the cost per call would be 18.31 / 31 = .59..... per minute.
the monthly cost for 87 minutes is $25.03.
if there were no fixed monthly charges, the cost per call would be 25.03 / 87 = .28..... per minute.
it appears there are some fixed charges per month that need to be accounted for.
if so, the fixed charges per month would be the same every month and the incremental charges per minute per month would be the same every month.
if we let f = the fixed charges per month and i equal the incremental charges per month and m equal the number of minutes used per month and c = the total cost per month, then the formula would be:
c = f + m * i.
the monthly cost for 31 minutes of calls is $18.31.
the formula for that becomes 18.31 = f + 31 * i.
the monthly cost for 87 minutes of calls is $25.03.
the formula for that becomes 25.03 = f + 87 * i.
we have 2 equations that need to be solved simultaneously.
they are:
18.31 = f + 31 * i
25.03 = f + 87 * i
subtract the first equation from the second to get:
25.03 - 18.31 = f - f + 87 * i - 31 * i
simplify to get:
6.72 = 56 * i
solve for i to get i = 6.72 / 56 = .12
the incremental cost per minute of calls is .12.
take any one of the two original equations and replace i with .12 to solve for f.
18.31 = f + 31 * i becomes 18.31 = f + 31 * .12 which becomes 18.31 = f + 3.72.
solve for f to get f = 18.31 - 3.72 = 14.59.
if we did this right, the fixed cost per month is 14.59 and the incremental cost per minute of calls is .12.
to confirm, we use these values in the two original equations.
18.31 = f + 31 * i becomes 18.31 = 14.59 + 31 * .12 which becomes 18.31 = 18.31 which is true.
25.03 = f + 87 * i becomes 25.03 = 14.59 + 87 * .12 which becomes 25.03 = 25.03 which is also true.
the solution is confirmed to be good.
the solution is that the fixed cost per month is 14.59 and the incremental cost per minute of calls per month is .12.
using this solution, the answer to the problem is that the monthly cost for 86 minutes of calls is 14.59 + 86 * .12 = 24.91.
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