M1M5L1 Business Cents

Introduction to systems of equations

• 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.

​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.

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?"