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.