UCSS Math I 3.2.3 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.
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