Mathematics
Grade 11
15 min
Add money amounts - word problems
Add money amounts - word problems
What you'll learn
- Solve word problems involving adding money amounts up to $10.00 with 80% accuracy.
- Identify the important information needed to solve money word problems in at least 3 out of 4 examples.
- Explain the steps they used to solve a money word problem to a partner, including using the words 'dollars' and 'cents'.
- Apply the dollar and cent symbols ($ and ¢) correctly when writing answers to money word problems in at least 4 out of 5 examples.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate complex financial word problems into a system of linear inequalities.
Define variables to represent quantities and constraints in a money-based scenario.
Accurately graph a system of linear inequalities to find a feasible region representing all possible financial outcomes.
Identify the vertices of a feasible region by solving systems of linear equations.
Formulate an objective function to represent profit, revenue, or cost.
Determine the optimal solution (e.g., maximum profit, minimum cost) by evaluating the objective function at the vertices of the feasible region.
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2
Key Concepts & Vocabulary
TermDefinitionExample
System of Linear InequalitiesA set of two or more linear inequalities containing the same variables. The solution to the system is the overlapping region that satisfies all inequalities simultaneously.A student has at most $50 to spend on notebooks (x) and pens (y). Notebooks cost $5 and pens cost $2. They must buy at least 8 items in total. The system is: `5x + 2y ≤ 50` and `x + y ≥ 8`.
ConstraintA limitation or restriction in a problem, which is expressed as a linear inequality.A bakery has a maximum of 100 hours of labor available per week. This is a constraint on production.
Feasible RegionThe solution set for a system of inequalities, represented graphically as the intersection of the shaded regions for each inequality. Any point (x, y) within this region is a v...
3
Core Formulas
Standard Form of a Linear Inequality
Ax + By \leq C \quad \text{or} \quad Ax + By \geq C
Used to represent constraints. 'x' and 'y' are the decision variables (e.g., number of items). 'A' and 'B' are the per-unit costs or values. 'C' is the total constraint value (e.g., total budget, total hours).
Objective Function for Optimization
f(x, y) = ax + by
This function represents the quantity you want to optimize. For a profit maximization problem, 'a' and 'b' would be the profit per unit for items 'x' and 'y', respectively. The goal is to find the (x, y) pair in the feasible region that results in the largest or smallest value for this function.
Corner Point Principle
\text{Maximum or...
4 more steps in this tutorial
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Challenging
A company manufactures two types of skateboards: Standard (x) and Pro (y). Profit is $20 per Standard and $30 per Pro. A Standard requires 1 hour in fabrication and 2 hours in finishing. A Pro requires 2 hours in fabrication and 2 hours in finishing. Fabrication has at most 8 hours available daily, and finishing has at most 12 hours. What is the maximum daily profit?
A.$120
B.$130
C.$140
D.$150
Easy
In the context of linear programming for financial problems, what is the term for the function that represents the quantity to be maximized or minimized, such as total profit or cost?
A.Constraint Function
B.Objective Function
C.Feasible Function
D.Vertex Function
Easy
When graphing a system of linear inequalities for a money problem, what is the name of the overlapping shaded region that contains all possible solutions satisfying all constraints?
A.Feasible Region
B.Solution Set
C.Constraint Area
D.Optimal Zone
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Frequently asked questions
What grade level is "Add money amounts - word problems"?
Add money amounts - word problems is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Add money amounts - word problems?
You'll be able to: Solve word problems involving adding money amounts up to $10.00 with 80% accuracy; Identify the important information needed to solve money word problems in at least 3 out of 4 examples; Explain the steps they used to solve a….
Is "Add money amounts - word problems" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Add money amounts - word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.