Question

The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 31 minutes of calls is $25.04 , and the remaining credit after 64 minutes of calls is $19.76 . What is the remaining credit after 85 minutes of calls?

Answer 1

Let the equation representing the function be y = -mx + c; where m is the charge per minute and c is a initial balance.
25.04 = -31m + c . . . . . (1)
19.74 = -64m + c . . . . . (2)
(1) - (2) gives: 5.3 = 33m
m = 5.3/33 = 0.16 (i.e. charge per minute is 16 cents)
From (1), 25.04 = -31(0.16) + c
25.04 = -4.96 + c
c = 25.04 + 4.96 = 30  (i.e. initial balance is $30)
Remaining credit after 85 minutes call is -85(0.16) + 30 = -13.6 + 30 = $16.40