A school supply company produces wooden rulers and plastic rulers. The rulers must first be made, and then painted. [list] [*]It takes 20 minutes to make a wooden ruler. It takes 15 minutes to make a plastic ruler. There is a maximum amount of 480 minutes per day set aside for making rulers. [*]It takes 5 minutes to paint a wooden ruler. It takes 2 minutes to paint a plastic ruler. There is a maximum amount of 180 minutes per day set aside for painting rulers. [/list] Write a system of inequalities that models the making and then painting of wooden and plastic rulers.

[list=1] [*]Identify the information you know. [*]Write an inequality to represent the amount of time needed to make the rulers. Let [i]w[/i] represent the wooden rulers and [i]p[/i] represent the plastic rulers. [*]Write an inequality to represent the amount of time needed to paint the rulers. Use the same variables to represent wooden and plastic rulers. [*]Now consider the constraints on this situation. It is not possible to produce a negative amount of either wooden rulers or plastic rulers; therefore, you need to limit the values of [i]w[/i] and [i]p[/i] to values that are greater than or equal to 0. [*]Combine all the inequalities related to the situation and list them in a brace, {. These are the constraints of your scenario. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCGPS Coordinate Algebra[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.

A school supply company produces wooden rulers and plastic rulers. The rulers must first be made, and then painted. [list] [*]It takes 20 minutes to make a wooden ruler. It takes 15 minutes to make a plastic ruler. There is a maximum amount of 480 minutes per day set aside for making rulers. [*]It takes 5 minutes to paint a wooden ruler. It takes 2 minutes to paint a plastic ruler. There is a maximum amount of 180 minutes per day set aside for painting rulers. [/list] Use the system of inequalities created in Example 3 to give a possible solution to the system.

[list=1] [*]We know from this situation that you cannot produce a negative amount of rulers, so none of our solutions can be negative. [*]In future lessons, we discuss more precise ways of determining the solution set to a system. For now, we can use our knowledge of numbers and ability to solve algebraic sentences to find possible solutions. [*]Choose a value for [i]w[/i]. Substitute the value for each occurrence of[i] w[/i] in the system and solve for [i]p[/i]. [*]Interpret the results. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCGPS Coordinate Algebra[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.