Answer:
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)](https://img.qammunity.org/2021/formulas/mathematics/high-school/jmf34gi28yzg63x728z9k1t64g5b2xd8b1.png)
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)](https://img.qammunity.org/2021/formulas/mathematics/high-school/3ew66nlrvf0wjvowno6o0uyd16bolbys5x.png)
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 \\\\](https://img.qammunity.org/2021/formulas/mathematics/high-school/10mcpwsrkfvnvo7adiberyiyfqlf4jfe3x.png)
[ 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](https://img.qammunity.org/2021/formulas/mathematics/high-school/uc5tjk0je8qd5z4lwrg9kslf99fsjaeqev.png)
From equation (ii),
![b=19.68-38*(-0.34)=32.6](https://img.qammunity.org/2021/formulas/mathematics/high-school/ke7pqlcpbe3j8to2ro8um6a81wmxk2o95z.png)
Putting the value od a and b in equation (i), we have
![y=-0.34x+32.6](https://img.qammunity.org/2021/formulas/mathematics/high-school/vmvo2tvoj4mxb1d32chmz8n0v17jk9j485.png)
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](https://img.qammunity.org/2021/formulas/mathematics/high-school/is7c9shxizobkzvtuqnoadcbwwex3wr1q9.png)
Hence, the remaining credit after 81 minutes of calls is $5.06.