## Running a Car Wash

**Work Time**

# Running a Car Wash

Maya is considering opening a car wash.

When you ride your car through the washer, you can get three different types of washes at three different prices: $11, $12.50, and $13.50.

When you wash your car yourself, the price depends on the time you spend. There is a base fee of $2 plus $ 0.75 per minute. On average, it takes about 6 minutes to clean a car.

- Graph
*y*= 11*x*,*y*= 12.5*x*, and*y*= 13.5*x*. The variable*x*is an independent variable, and*x*runs from 0 to 50. - Maya wants to know how many of each type of car wash are needed to make $500.00 from each type of wash. Solve this problem using the graphs.
- Maya wants to get an easy formula for how much she will earn from the self-wash section. Her friend Karen suggests the formula
*y*= 6.5*x*. Draw Karen's graph on the same coordinate grid. Discuss with a partner what the four graphs tell you about the money Maya makes when she gets about 50 cars per day, each using one of the four types of wash.

Finally, after reflecting all options she decides to draw a fifth graph on the coordinate grid. The fifth graph is shown on the right.

What price per car does Maya charge, according to this graph?

There is also another formula that Maya uses for her car wash:

*y*= 0.75*x*+ 2- Explain the meaning of this formula.
- Create the graph.
- Is this the graph of a proportional relationship?