SOLUTION: The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes), as shown in the figure below. The remaining credit

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Question 98403: The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes), as shown in the figure below. The remaining credit after 23 minutes of calls is $21.78 , and the remaining credit after 57 minutes of calls is $17.02 . What is the remaining credit after 87 minutes of calls?

Found 2 solutions by checkley71, mathslover:
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
(57-23)M=17.02-21.78
34M=-4.76
M=-4.76/34
M=-.14 PER MINUTE USED
87-57=30 MINUTES USED. THEREFORE THE REDUCTION IN CREDIT IS:
30*-.14=-4.20
17.02-4.20=$12.82 CREDIT REMAINING ON THE CARD AFTER 87 MINUTES ARE USED.

Answer by mathslover(157) (Show Source):
You can put this solution on YOUR website!
let the total credit C after M minutes of call be given by
C = $(a*M + b) where a and b are some constants.
So we have:
21.78 = a * 23 + b (1) and
17.02 = a * 57 + b (2)
Subtracting equation (2) from (1):
4.76 = -34a
a = -4.76/34
= -.14
Putting this value of a in equation (1):
21.78 = -.14 * 23 + b
therefore, b = 21.78 + 3.22
= 25
So the linear equation for the credit remaining after M minutes of call is
C = $(-.14 * M + 25)
So, the remaining credit after 87 minutes
C = -.14 * 87 + 25
= $12.82