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 38 minutes of calls is $ 25.06, and the remaining credit after 69 minutes of calls is $21.03. What is the remaining credit after 80 minutes of calls?

Answer 1

Answer: $19.6

Step-by-step explanation:

Linear function: f(x)=mx+c

, where  m= rate of change in f(x) with respect to x.

c = Initial value.

Let c = Initial value of card , m= Charge per minute

x= Number of minutes calling time.

Then, 25.06= 38m+c   (i)

21.03=69m+c (ii)

Eliminate (ii) from (i)

$4.03=-31m\\\\\Rightarrow\ m=\dfrac{4.03}{-31}\\\\\Rightarrow\ m=-0.13$

Put m in (i) , we get

$25.06= 38(-0.13)+c\\\\\Rightarrow\ 25.06=-4.94+c\\\\\Rightarrow\ c=25.06+4.94\\\\\Rightarrow\ c=30$

i.e. f(x)=-0.13x+30

if x=80 then

f(80)= -0.13(80)+30

=-10.4+30

=19.6

Hence, the remaining credit after 80 minutes of calls = $19.6