Chapter 1.1, Problem 47E

Solution

a)

To find: How much does E has to pay if she rented the car for one day and drove 83 mi.

E has to pay $\$46.94$ .

Given Information:

Swan Auto Rental charges $32 per day plus $0.18 per mile for an automobile rental.

E rented a car for one day and drove 83 mi.

Concept used:

Let $x$ be the number of days the car is rented and $y$ be the distance travelled in miles.

Then, the total rental charges for $x$ days and $y$ distance is given by $C=32x+0.18y$ .

Calculation:

Now, E rented a car for one day and drove 83 mi implies that $x=1$ and $y=83$ .

Substitute 1 for $x$ and 83 for $y$ into $C=32x+0.18y$ .

  $\begin{array}{c}C=32\left(1\right)+0.18\left(83\right)\\ =32+14.94\\ =46.94\end{array}$

Therefore, E has to pay $\$46.94$ .

b)

To calculate: The distance R drove the rented car.

R drove 210 miles.

Given Information:

Swan Auto Rental charges $32 per day plus $0.18 per mile for an automobile rental.

R paid $\$69.80$ to rent a car for one day.

Concept used:

Let $x$ be the number of days the car is rented and $y$ be the distance travelled in miles.

Then, the total rental charges for $x$ days and $y$ distance is given by $C=32x+0.18y$ .

Calculation:

Now, R rented a car for one day implies that $x=1$ .

Substitute 1 for $x$ and $69.8$ for $C$ into $C=32x+0.18y$ .

  $\begin{array}{c}69.8=32\left(1\right)+0.18y\\ 69.8=32+0.18y\\ 69.8-32=0.18y\\ 210=y\end{array}$

Therefore, R drove 210 miles.