Two Variables

Inequalities are equations that can be used to determine not just what something could equal but what something cannot equal. It tells us what the relative size is of two values and if they are big or small, too much or not enough. Inequalities could make it easier to determine how much someone might need of something in order to make a certain amount of something, while also determining how much more might be needed or how much be left. For example, if someone wanted to make cupcakes and flat cakes, they would need a specific amount of flour for each cake and cupcake. However, if they only have 12 cups of flour and cupcakes take one cup while cakes take two cups of flour an inequality would be needed to determine if there is enough flour to make 30 cupcakes and 2 flat cakes. The inequality would then be able to determine whether or not there was enough flour and if not how much more would be needed. There is a company called Ozark Furniture that specializes in making rocking chairs. They make classical and modern rocking chairs, both of which require the same type of lumber, maple; therefore, it is important to know how many of each chair they can make with the amount of lumber at one time is 3000 board feet. However, how many classical and modernized rocking chairs are they able to make from that lumber? If they made an inequality, they could determine how and if 3000 board feet of lumber is enough to make the amount of chairs they want. We will use “c” to represent the classic rockers and “m” for the modern rockers. Here we are given that a classic maple rocker requires 15 board feet of maple, and a modern rocker requires 12 board feet of maple. We have “c” classic maple rocker, so total maple required for classic maple rocker chair = 15c board feet. With “m” modern maple rocker, a total required for classic maple rocker chair = 12m board feet. We have a total maple available is 3000 board feet.

Together the inequality will look like this: