Subjects algebra

Budget Constraint

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Budget Constraint


1. **State the problem:** Marsha has 300 money units to spend on paper, pencils, and pens. Prices are: - Paper: 20 per box - Pencils: 10 per package - Pens: 35 per package with 10% discount, so pens cost: $$35 - (0.10 \times 35) = 35 - 3.5 = 31.5$$ 2. **Write the budget constraint:** If $x, y, z$ are the number of boxes/packages of paper, pencils, and pens respectively, then: $$20x + 10y + 31.5z \leq 300$$ 3. **Graph interpretation:** A triangle is formed with vertices at (0,0), (4,0), and (4,3) showing possible combinations. Likely these coordinates represent maximum quantities of two items under certain constraints. 4. **Check the triangle's base and height:** Base from (0,0) to (4,0) means maximum $x=4$ when items on the axis vary; height up to $y=3$ at $x=4$ might represent upper limit for other items. 5. **Summary:** The graph helps visualize the feasible region for spending on the items given the budget and prices. Final budget inequality is: $$20x + 10y + 31.5z \leq 300$$ The triangle relates likely to constraints on $x$ and $y$ with $z$ fixed or 0. Thus, Marsha can buy combinations $(x,y,z)$ satisfying this inequality within her total 300 budget.