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Applications of Linear Systems

Word problems using two equations and two unknowns

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The Perfect Hue

Credit: Patrick M. Kearney/U.S. Navy
Source: http://commons.wikimedia.org/wiki/File:US_Navy_070823-N-9195K-025_Aerographer's_Mate_1st_Class_William_Palmer_uses_a_roller_to_add_a_second_coat_of_paint_to_a_wall_during_a_community_relations_project_at_Voza_Medical_Clinic_in_support_of_Pacific_Partnership.jpg
License: CC BY-NC 3.0

Have you ever painted a room? Before you start painting, you have to carefully choose a color. You then head over to a hardware or paint store and ask the staff to mix the color for you. The store doesn’t keep every color in stock at all times. How can the staff mix up the right color on a moment’s notice?

Mixing Machines

At most large stores, staff members use a mixing machine to create your paint. Paint consists of a base and pigment. The base is usually white. It gives the paint body and helps it stick to the wall. The pigment gives the paint its color. By carefully combining pigments, the store can produce almost any color imaginable. The mixing machine uses systems of equations to determine how much of each pigment to use in order to produce a set amount of a given color. More pigment makes brighter, darker colors. Less pigment makes lighter colors. The store’s staff members know how to program the machine to create the color you want. They’ll also leave a drop of paint on the lid of your newly made can to show the color of the paint after drying. Liquid paint often appears to be a different color than dried paint, so it’s important to pay attention to those dots.

Credit: The White House
Source: http://commons.wikimedia.org/wiki/File:White-house-floor1-green-room.jpg
License: CC BY-NC 3.0

When you’re decorating a room, it’s important to choose your colors carefully. Paint is expensive, so you’ll want to opt for colors you can live with for a long time. Scientists have studied how different colors affect the brain. Red rooms actually cause students to perform worse on exams, while green rooms improve reading comprehension scores. Pink walls calm people down for short periods of time but make them angry in the long run. Blue walls can control appetite, and yellow walls can make adults anxious and babies cry.

See for yourself: http://www.hgtv.com/decorating/10-tips-for-picking-paint-colors/index.html

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Watch the videos at the first two links below to learn how to paint a wall and test paint colors. Check out the last clip to see a high-tech paint that can change color.




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