Respuesta :
Answer:
5.06
Step-by-step explanation:
Given that the remaining credit after 38 minutes of calls is 19.68, and the remaining credit after 60 minutes of calls is 12.20.
As the credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes), so let the linear equation be
[tex]y=ax+b\cdots(i)[/tex]
where y is the credit remaining on a phone card (in dollars) and x is the total calling time made with the card (in minutes).
Now, as the remaining credit after 38 minutes of calls is 19.68, so, put x=38 and y=19.68 in equation (i), we have
[tex]19.68=38a+b \\\\\Rightarrow b= 19.68-38a\cdots(ii)[/tex]
Similarly, the remaining credit after 60 minutes of calls is 12.20, so, put x=60 and y=12.20 in equation (i), we have
[tex]12.20=60a+b \\\\[/tex]
[tex]\Rightarrow 12.20=60a+(19.68-38a)[/tex] [ by using (ii)]
[tex]\Rightarrow 12.20=60a+19.68-38a \\\\\Rightarrow 22a=12.20-19.68=-7.48 \\\\\Rightarrow a=-7.48/22=-0.34[/tex]
From equation (ii),
[tex]b=19.68-38\times(-0.34)=32.6[/tex]
Putting the value od a and b in equation (i), we have
[tex]y=-0.34x+32.6[/tex]
So, the remaining credit after 81 minutes can be determined by putting x=81 in the above equation.
[tex]y=-0.34\times 81 +32.6 \\\\ \Rightarrow y=5.06[/tex]
Hence, the remaining credit after 81 minutes of calls is $5.06.
