Chapter 8.3, Problem 48E

To determine

To write and graph:

Anequationdescribing the possible numbers of basic and deluxe washes that could have been done. Give three possible combinations of deluxe and basic car washes.

Answer to Problem 48E

The three possible combination of washes would be 15 basic washes and 70 deluxe washes, or 30 basic washes and 60 deluxe washes, or 60 basic washes and 40 deluxe washes.

Explanation of Solution

Given:

A car wash charges $8 for a basic wash and $12 for a deluxe wash that includes wax. On a certain day, sales at the car wash total $960.

Calculation:

Let x represent number of basic car washes and y represent number of deluxe car washes.

We have been given that a car wash charges $8 for a basic wash, so amount earned from x basic car washes would be $8x$ .

We have been given that a car wash charges $12 for a deluxe wash, so amount earned from ydeluxe car washes would be $12y$ .

Since total amount earned i$960, so we will set amount earned from x basic car washes and y deluxe car washes equal to $960 as:

  $8x+12y=960$

We will use intercepts to graph our equation.

  $\begin{array}{l}8x+12y=960\left(\text{Given equation}\right)\\ 8x+12(0)=960\left(\text{Substituting }y=0\right)\\ 8x=960\\ \frac{8x}{8}=\frac{960}{8}\left(\text{Dividing both sides by }8\right)\\ x=120\end{array}$

Therefore, the x -intercept of our given equation is $(120,0)$ .

To find y- intercept, we will substitute $x=0$ in our given equation and solve for yas shown below:

  $\begin{array}{l}8x+12y=960\left(\text{Given equation}\right)\\ 8(0)+12y=960\left(\text{Substituting }x=0\right)\\ 12y=960\\ \frac{12y}{12}=\frac{960}{12}\left(\text{Dividing both sides by }12\right)\\ y=80\end{array}$

Therefore, the y -intercept of our given equation is $(0,80)$ .

Upon graphing our given equation, we will get our required graph as shown below:

  

Upon looking at our graph, we can see that points (15,70), (30,60), and (60,40) lie on the line. Therefore, the three possible combination of washes would be 15 basic washes and 70 deluxe washes, or 30 basic washes and 60 deluxe washes, or 60 basic washes and 40 deluxe washes.