Below shows multiple ways to answer the questions to this problem.
Let \(x=\) pounds of rice, \(y=\) pounds of beans.
Table
| \(x\) (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 |
| 0 | 60 | 90 | 720 ok |
Graph
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.
\(2x+1.5\leq100\) dollars
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
\(8x+12y\leq500\) servings
We also can’t have negative pounds or beans or rice so,
\(x\geq0, \, y\geq0\)
Graph using Desmos.com
