CCGPS CA 2.3.2 Example 4

An artist wants to analyze the time that he spends creating his art. He makes oil paintings and watercolor paintings. The artist takes 8 hours to paint an oil painting. He takes 6 hours to paint a watercolor painting. He has set aside a maximum of 24 hours per week to paint his paintings. The artist then takes 2 hours to frame and put the final touches on his oil paintings. He takes 3 hours to frame and put the final touches on his watercolor paintings. He has set aside a maximum of 12 hours per week for framing and final touch-ups. Write a system of inequalities that represents the time the artist has to complete his paintings. Graph the solution.
  1. Create the system of inequalities. Let x = the number of oil paintings he makes. Let y = the number of watercolor paintings he makes.
  2. Graph the system on the same coordinate plane.
  3. The solution is the overlapping shaded region; any points that lie within it are solutions to the system.
This applet is provided by Walch Education as supplemental material for the CCGPS Coordinate Algebra program. Visit www.walch.com for more information on our resources.