Below shows multiple ways to answer the questions to this problem.
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|
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,
\(x\geq0, \, y\geq0\)
Graph using Desmos.com