Algebra 2 question

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
24
minutes of calls is
$22.12
, and the remaining credit after
60
minutes of calls is
$17.80
. What is the remaining credit after
86
minutes of calls?

Answer 1

Hello,

So given this information you must find the difference between the 24 minutes of calls and the 60 minutes. 

If you only had the first 24 minutes of information and nothing else, then you wouldn't be able to solve since there is nothing to base the amount off of. Since this isn't the case we can figure the difference in minutes and money and calculate how much each minute is worth.

 

Step 1)   60 - 24 = 36 minute difference

Step 2 ) 22.12 - 17.80 = 4.32

(please not that these numbers do not have to be respective because we are only calculating the difference)

 

This means that using between using this 36 minutes of data, we used 4.32 off of the card.

we divide 4.32 by 36 to calculate the cost per minute 

Step 3) 4.32 / 36 = .12 or 12 cents per minute.

Step 4) since we know that per minute it is 12 cents, we figure out now how many more minute than 60 it is that we have used off of our card            86-60 = 26 

Step 5) Now that I have the cost per minute and the extra number of minutes I multiply those 2 numbers

.12 x 26 = 3.12 

Step 6) Finally take this additional card usage value and subtract from the amount of money the card had on it when from the minute value we compared to 86   (which was 60 minutes) and we come up with 17.80-3.12 = $14.68