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 19.68, and the remaining credit after 60 minutes of calls is . What is the remaining credit after 81 minutes of calls?

Answer 1

5.06

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

`y=ax+b\cdots(i)`

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

`19.68=38a+b \\\\\Rightarrow b= 19.68-38a\cdots(ii)`

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

`12.20=60a+b \\\\`

`\Rightarrow 12.20=60a+(19.68-38a)` [ by using (ii)]

`\Rightarrow 12.20=60a+19.68-38a \\\\\Rightarrow 22a=12.20-19.68=-7.48 \\\\\Rightarrow a=-7.48/22=-0.34`

From equation (ii),

`b=19.68-38*(-0.34)=32.6`

Putting the value od a and b in equation (i), we have

`y=-0.34x+32.6`

So, the remaining credit after 81 minutes can be determined by putting x=81 in the above equation.

`y=-0.34* 81 +32.6 \\\\ \Rightarrow y=5.06`

Hence, the remaining credit after 81 minutes of calls is $5.06.