Beans in multiple representations
Let’s look at a table of values…
Let \(x=\) pounds of rice, \(y=\) pounds of beans.
|x(lbs rice)||y(lbs beans)||$||Servings|
|0||0||0 ok||0 no|
|0||10||15 ok||120 no|
|0||20||30 ok||240 no|
|0||40||60 ok||480 no|
|0||50||75 ok||600 ok|
This is getting tedious…so let’s move on to equations…,
Each lb of rice costs $2, so rice cost is \(2x\).
Each lb of beans, cost $1.5, so beans cost is \(1.5y\).
Total cost is \(2x+1.5y\) and we want that to be no more than $100.
Similarly, we can serve 8 people, for every lb of rice, 8x servings.
And we can serve 12 people for every lb of beans, \(12y\) servings.
We want to have at least 500 servings or
We also can’t have negative pounds or beans or rice so,
\(x\geq0, \, y\geq0\)
Let’s use desmos.com to graph these inequalities: