Chapter 3, Problem 37RE

(a).

To determine

Linear function that relates cost $c$ to total minutes on the phone, $x$ for each company.

Answer to Problem 37RE

Linear function that relates cost $c$ to total minutes on the phone, $x$ for each company is $C_1\left(x\right)=7+0.06x$ and $C_2\left(x\right)=0.08x$ .

Explanation of Solution

Given:

  $\$7.00$ plus $\$0.06$ per minute.

Monthly fee charges $\$0.08$ per minute.

Calculation:

Marissa spent $x$ minutes on phone.

Company $A$ charges monthly fees of $\$7.00$ dollars plus $\$0.06$ per minute..

Company $B$ charges only $\$0.08$ per minute.

Let, $C_1\left(x\right)$ and $C_2\left(x\right)$ be the cost function of company $A$ and company $B$ . Then we get:

  $C_1\left(x\right)=7+0.06x$ and $C_2\left(x\right)=0.08x$

Where,

  $x$ represents total minutes used.

Conclusion:

Thus, $C_1\left(x\right)=7+0.06x$ and $C_2\left(x\right)=0.08x$

(b).

To determine

Number of minutes $x$ for which the bill from company $A$ will equal $x$ the bill from company $B$ .

Answer to Problem 37RE

  $350\min utes$ is used then the bill from company $A$ will equal the bill from company $B$ .

Explanation of Solution

Given:

  $\$7.00$ plus $\$0.06$ per minute.

Monthly fee charges $\$0.08$ per minute.

Calculation:

Let,

  $C_1\left(x\right)=C_2\left(x\right)$

Then we get:

  $\begin{array}{l}7+0.06x=0.08x\\ \left(0.08-0.06\right)x=7\end{array}$

Equivalent to,

  $\begin{array}{l}x=\frac{7}{0.08-0.06}\\ =\frac{7}{0.02}\\ =350\end{array}$

Thus, marrisa spent $350$ minutes to get equal bill amounts.

Conclusion:

That is why $350\min utes$ is used then the bill from company $A$ will equal the bill from company $B$ .

(c).

To determine

Interval of minutes $x$ will the bill from company $B$ be less than bill from company $A$ .

Answer to Problem 37RE

Then the bill from company $B$ is less than the bill from company $A$ .

Explanation of Solution

Given:

  $\$7.00$ plus $\$0.06$ per minute.

Monthly fee charges $\$0.08$ per minute.

Calculation:

Let,

  $C_1\left(x\right)=C_2\left(x\right)$

Then we get:

  $\begin{array}{l}7+0.06x=0.08x\\ 0.02x<7\end{array}$

Which implies,

  $\begin{array}{l}x<\frac{7}{0.02}\\ =350\end{array}$

  $x$ must be non negative value because time cannot be negative.

That is why needed answer is $\left[0,350\right)$

That is if, $0\le x<350$ .

Conclusion:

That is why Then the bill from company $B$ is less than the bill from company $A$ .