Chapter 3.1, Problem 37AYU

(a)

To determine

To find: the rent of the truck to drive 40 miles

Answer to Problem 37AYU

The cost of renting a moving truck to drive 40 miles is $\text{\$}45$ .

Explanation of Solution

Given:

  $C\left(x\right)=0.25x+35$

  $x=40\text{ miles}$

Calculation:

To find the rent of the truck to drive 40 miles, find $C\left(40\right)$ .

Substitute 40 for x in $C\left(x\right)=0.25x+35$

  $\begin{array}{l}C\left(40\right)=0.25\left(40\right)+35\\ \text{ =}10+35\\ \text{ =}45\end{array}$

Conclusion:

Therefore, the cost of renting a moving truck to drive 40 miles is $\text{\$}45$ .

(b)

To determine

To find: the distance he drivesif the cost of renting the moving truck is $\$80$ .

Answer to Problem 37AYU

180 miles can be driven by paying $80 as the rent.

Explanation of Solution

Calculation:

Substitute $\$80$ for $C\left(x\right)$ in the equation $C\left(x\right)=0.25x+35$ .

  $80=0.25x+35$

Subtract 35 from both the sides.

  $\begin{array}{l}80-35=0.25x+35-35\\ 45=0.25x\end{array}$

Swap the sides of the equation.

  $0.25x=45$

Divide both the sides by 0.25.

  $\begin{array}{l}\frac{0.25x}{0.25}=\frac{45}{0.25}\\ \Rightarrow x=180\end{array}$

Conclusion:

Therefore, 180 miles can be driven by paying $80 as the rent.

(c)

To determine

To find: The maximum number of miles that can be driven

Answer to Problem 37AYU

The maximum number of miles that can be driven by paying no more than $100 is 260 miles.

Explanation of Solution

Calculation:

Since the cost should not be more than $\$100$ , the cost can be expressed as an inequality as $C\left(x\right)\le \text{1}00$ .

  $\begin{array}{l}C\left(x\right)\le 100\\ 0.25x+35\le 100\end{array}$

Subtract 35 from both sides of the inequality.

  $\begin{array}{l}0.25x+35-35\le 100–35\hfill \\ 0.25x\le 65\hfill \end{array}$

Divide both the sides by 0.25.

  $\begin{array}{l}\frac{0.25x}{0.25}\le \frac{65}{0.25}\\ \Rightarrow x\le 260\end{array}$

Conclusion:

Therefore, the maximum number of miles that can be driven by paying no more than $100 is 260 miles.

(d)

To determine

To describe: the implied domain of C .

Answer to Problem 37AYU

The implied domain of C is $\text{Domain : }\left[0,\infty \right]$ .

Explanation of Solution

Calculation:

  $\begin{array}{l}C\left(x\right)=0.25x+35\\ \text{Domain : }\left[0,\infty \right]\end{array}$

Conclusion:

Therefore, the implied domain of C is $\text{Domain : }\left[0,\infty \right]$ .