Chapter 6.8, Problem 7STP

To determine

To calculate: The total cost to drive her car on the vacation.

The cost to drive her car $\$100$ , plus between $\$0.50\text{ and }\$0.75$ per mile. If she will drive her car $400$ miles what is the conclusion about $c$ .

Answer to Problem 7STP

The total cost to drive her car is: $300\prec c\prec 400$ option $A$ is correct.

Explanation of Solution

Given information:

The cost to drive her car $\$100$ , plus between $\$0.50\text{ and }\$0.75$ per mile. If she will drive her car $400$ miles what is the conclusion about $c$ .

The options are:

  $\begin{array}{l}\text{A 300}\prec \text{c}\prec \text{400 C 100}\prec \text{c}\le \text{400}\\ \text{B 200}\prec \text{c}\le \text{400 D 200}\le \text{c}\le \text{300}\end{array}$

Calculation:

Considered the statement, The cost to drive her car $\$100$ , plus between $\$0.50\text{ and }\$0.75$ per mile. If she will drive her car $400$ miles what is the conclusion about $c$ .

The cost to drive her car: $\$100$ ,

The cost of mile: $\$0.50\text{ and }\$0.75$ .

Total miles she will drive her car: $400$ ,

The consolation about $c$ is: $?$

As the responsible total cost with multiple of additional amount added to $\$100$ miles by the $400$ miles drive.

Now the lowest amount added for $400$ miles:

  $0.50\left(400\right)=200$

Same as here the highest amount for

  $400$ miles:

  $0.75\left(400\right)=300$

Here if there is a addition of $100$ to the both sides, I would get the result in between $300\text{ and }400$ .

Therefore, the conclusion for the total cost to drive the car on the vacation is: $300\prec c\prec 400$ .

Hence, the conclusion for the total cost to drive: $3{\left(2x+1\right)}^2=27$ is $x=-2,x=1$ , option $B$ is correct.