Chapter 3.6, Problem 9P

To determine

To find:therate of phone call for first minute and each other minute.

Answer to Problem 9P

The rate of phone call for first minute and each other minute are $2.80 and $1.20, respectively.

Explanation of Solution

Given information:

The rate of phone call at one rate for first minute and at a different rate for each other minute.

The call cost of 7 minutes is $10 and the call cost of 4 minute is $6.40.

Calculation:

Let x be a rate phone call for first minute and let y be the rate of phone call for each other minutes.

Here, x is a fixed minute for all calls

  $\text{cost}=x+y\left(\text{remaining minutes}\right)$

The call cost of 7 minutes is $10 can be converted into equation,

  $\begin{array}{l}10=x+y\left(7-1\right)\\ x+6y=10\end{array}$

The call cost of 4 minute is $6.40can be converted into equation,

  $\begin{array}{l}6.4=x+y\left(4-1\right)\\ x+3y=6.4\end{array}$

Compute the solutions of the system $x+6y=10$ and $x+3y=6.4$ by linear combination method.

Subtract the equations $x+3y=6.4$ from $x+6y=10$ , simplify further.

  $\begin{array}{l}x+6y=10\\ x+3y=6.4\\ \overline{0x+3y=3.6}\end{array}$

Divide on both sides by3,

  $\begin{array}{l}\frac{3y}{3}=\frac{3.6}{3}\\ y=1.2\end{array}$

Substitute $y=1.2$ in $x+6y=10$ and simplify the value of x ,

  $\begin{array}{l}x+6\left(1.2\right)=10\\ x+7.2=10\\ x=10-7.2\\ x=2.8\end{array}$

Therefore, the rate of phone call for first minute and each other minute are $2.80 and $1.20, respectively.