M1M5L1 Business Cents

Graphing

Warm up #1

Graph the line $$y=\frac{-1}{3}x+3$$ .

Graphing

Warm up #2

Graph the line $$y=\frac{3}{2}x$$ .

Math Response

Warm up #3

If $$4p=12$$ then $$p=?$$

Type answer here

Correct Answer: 3

Deg^°

Rad

Math Response

Warm up #4

If $$5p=10$$ then $$p=?$$

Type answer here

Correct Answer: 2

Deg^°

Rad

Business Cents

Introduction to systems of equations

​Learning Focus

• What is a system of equations and what does it's solution look like?

• How do I solve systems of equations represented by a context?

• How do I use the solution to the system of equations to make decisions?

The Martinez twins, Carlos and Clarita, are trying to find a way to make money during summer vacation. When they overhear their aunt complaining about how difficult it is to find someone to care for her pets while she will be away on a trip, Carlos and Clarita know they have found the perfect solution. Not only do they have a large, unused storage shed on their property where they can house animals, they also have a spacious fenced backyard where the pets can play.

Carlos and Clarita need to clean the storage shed where they plan to board the pets. They have decided to hire a company to clean the windows. After collecting the following information, they have come to you for help deciding which window cleaning company they should hire.

Sunshine Express Window Cleaners charges $50 for each service call, plus $10 per window.

“Pane”less Window Cleaners charges $25 for each service call, plus $15 per window.

​Launch

Open Ended

Which company would you recommend, and why? Prepare an argument to convince Carlos and Clarita that your recommendation is reasonable. (It is always more convincing if you can support your claim in multiple ways. How might you support your recommendation using a table? A graph? Algebra?)

I think Carlos and Clarita should choose ___________, because _________.

​Once the windows are clean, Carlos and Clarita also want to have the window frames repainted to make the storage shed look more appealing to potential customers. They have decided to hire a company to paint the windows. Again, they need your help deciding which painter they should hire.

Paint by Numbers charges for $100 sanding the frames and masking the windows with tape, and $16 per hour for painting, since different employees do different parts of the work.

Paint it Right charges $24 per hour for all labor, plus a $38 waste disposal fee.

​Explore

Open Ended

Which company would you recommend, and why? Prepare an argument to convince Carlos and Clarita that your recommendation is reasonable. (Support your claim in multiple ways including a table, a graph, and algebra.)

I think Carlos and Clarita should choose ___________, because _________.

Both pain companies allow the customer to purchase their own paint supplies. Carlos has done some research and found the following information:

Handyman Tools and Supplies sells a small painter’s kit that contains 2 paint brushes and 4 rolls of masking tape for $16. They also sell a large painter’s kit that contains 5 paint brushes and 15 rolls of masking tape for $50.

Carlos’s dad is planning to paint a couple of rooms in their house, and has offered to buy any left-over supplies. Carlos is trying to figure out how much he would charge his dad for each paint brush and each roll of tape. To keep track of the information, he has written the following equations:
2p+4r=16
5p+15r=50

Clarita is looking at Carlos's notes and asks, "What do p and r stand for?" 

Open Ended

In the following system of equations, Clarita wants to know, "What do p and r stand for?"

2p+4r=16
5p+15r=50

How would you answer Clarita's question?

Graphing

In the previous two questions you discovered (hopefully) that $$\left(4,0\right)$$ and $$\left(0,8\right)$$ are solutions to the linear equation $$2p+4r=16$$ . Graph the line by plotting the points.

Graphing

Graph the linear function $$p=-3r+10$$ by plotting the y-intercept as the first point and using the slope to find a second point (treat r as an x and p as a y).

Fill in the Blanks

Fill in the Blanks

Retrieval

Graphing

Graph the linear function $$y=-\frac{3}{2}x+1$$ .

Graphing

Graph the linear function $$y=-\frac{2}{3}x-1$$ .