Mathematics
Grade 11
15 min
Divide money amounts
Divide money amounts
What you'll learn
- Solve word problems involving dividing money amounts equally among a group of people, using drawings or equations, with at least 80% accuracy.
- Explain how to divide a dollar amount into smaller equal parts, using terms like 'half,' 'quarter,' and 'cents' in their explanation.
- Identify the correct amount of money each person receives when a given amount is divided equally, demonstrating understanding by correctly answering at least 3 out of 4 questions.
- Apply division strategies to determine how many of a specific item (e.g., stickers, candy) each person gets when a given dollar amount is used to purchase them, solving at least 2 problems correctly.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate real-world scenarios about dividing money into systems of linear inequalities.
Define variables and write constraint inequalities based on given financial conditions.
Graph systems of linear inequalities to identify the feasible region representing all possible solutions.
Formulate an objective function to represent a financial quantity to be maximized or minimized.
Identify the vertices of the feasible region by solving systems of linear equations.
Evaluate the objective function at each vertex to find the optimal solution for dividing a money amount.
Interpret the optimal solution in the context of the original financial problem.
How does a business decide how to divide its budget between marketing and product development to get the most pro...
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Key Concepts & Vocabulary
TermDefinitionExample
System of Linear InequalitiesA set of two or more linear inequalities containing the same variables. In financial problems, this system defines all the rules or limits on how money can be divided.An investor has up to $10,000. Let x be money in stocks and y be money in bonds. The system might include: x + y ≤ 10000, x ≥ 2000, y ≥ 3000.
ConstraintsThe inequalities within the system that represent limitations or conditions in the problem, such as budget limits, minimum investment amounts, or production requirements.The constraint 'the total amount invested cannot exceed $50,000' is written as x + y ≤ 50000.
Feasible RegionThe solution set for the system of inequalities, represented by the overlapping shaded area on a graph. Any point (x, y) within this region...
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Core Formulas
Constraint Inequality Forms
Ax + By ≤ C or Ax + By ≥ C
Used to model the limitations in a problem. 'x' and 'y' are the amounts of money allocated to two different options. 'A' and 'B' are coefficients (like cost per item), and 'C' is the total limit (like a total budget).
Objective Function Formula
Z = ax + by
Used to define the quantity to be optimized. 'Z' could represent Profit (P), Cost (C), or Return (R). 'a' and 'b' are the contributions of each variable to the total (e.g., profit per unit).
Non-Negativity Constraints
x ≥ 0 and y ≥ 0
These are fundamental constraints in most money-division problems because you cannot invest a negative amount of money or produce a negative number...
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Easy
In the context of dividing money using linear programming, what does the 'feasible region' represent on a graph?
A.The single point that represents the maximum possible profit.
B.The area containing all possible ways to divide the money that satisfy all the given constraints.
C.The line that represents the objective function.
D.The set of points that represent impossible ways to divide the money.
Easy
What is the primary purpose of an objective function in a financial linear programming problem?
A.To set the budget limit for the investment.
B.To define the boundaries of the feasible region.
C.To represent the financial quantity (like profit or cost) that is to be maximized or minimized.
D.To ensure that the money amounts invested are not negative.
Easy
A student is setting up a system of inequalities for a problem about dividing money between two accounts, x and y. Which of the following are the standard non-negativity constraints?
A.x + y > 0
B.x > 0 and y > 0
C.x + y ≤ 0
D.x ≥ 0 and y ≥ 0
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Frequently asked questions
What grade level is "Divide money amounts"?
Divide money amounts is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Divide money amounts?
You'll be able to: Solve word problems involving dividing money amounts equally among a group of people, using drawings or equations, with at least 80% accuracy; Explain how to divide a dollar amount into smaller equal parts, using terms like….
Is "Divide money amounts" free to practice?
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How many practice questions are included with Divide money amounts?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.