# UCSS Math I 3.2.3 Example 4

- Author:
- Walch Education

- Topic:
- Inequalities

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.

- Create the system of inequalities. Let
*x*= the number of oil paintings he makes. Let*y*= the number of watercolor paintings he makes. - Graph the system on the same coordinate plane.
- The solution is the overlapping shaded region; any points that lie within it are solutions to the system.

*UCSS Secondary Math I*program. Visit www.walch.com for more information on our resources.