Mathematics
Grade 11
15 min
Purchases - do you have enough money - up to $10
Purchases - do you have enough money - up to $10
What you'll learn
- Solve word problems to find the total cost of up to three items, each costing less than $10, with 80% accuracy.
- Determine if they have enough money (up to $10) to purchase a set of items by comparing the total cost to the amount of money available, and explain their reasoning.
- Calculate the amount of money remaining after a purchase (up to $10) with at least 70% accuracy.
- Identify the coins and bills needed to make a purchase up to $10 with 90% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate real-world purchasing scenarios with a budget up to $10 into a system of linear inequalities.
Accurately graph a system of linear inequalities on the Cartesian plane, identifying the boundary lines and correct shading.
Determine the feasible region representing all possible purchase combinations that satisfy the given constraints.
Interpret the vertices of the feasible region in the context of the purchasing problem.
Apply integer constraints to find all possible discrete solutions within a feasible region.
Analyze a system to determine if a specific purchase combination is possible given the budget and other constraints.
You have a $10 bill for the snack bar. Can you buy 2 slices of pizza and 3 sodas? Let's use advanced math to find out!...
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 set of all ordered pairs (x, y) that satisfy all inequalities simultaneously.You have $10. Apples (x) cost $1 and bananas (y) cost $0.50. You must buy at least 5 fruits. The system is: `1x + 0.50y ≤ 10` and `x + y ≥ 5`.
ConstraintA condition, expressed as an inequality, that limits the possible values of the variables in a problem. Common constraints include budget, time, or quantity.The constraint `1.50x + 2.00y ≤ 10` means the total cost of item x and item y cannot exceed $10.00.
Feasible RegionThe area on a graph that contains all the points satisfying every inequality in the system. It is the overlapping shaded region of all the i...
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Core Formulas
Standard Form of a Linear Inequality
Ax + By \leq C \quad or \quad Ax + By \geq C \quad or \quad Ax + By < C \quad or \quad Ax + By > C
This is the standard way to write a linear inequality in two variables, x and y. A, B, and C are constants. This form is essential for setting up the constraints of your purchasing problem, where C often represents the total budget ($10 in our case).
Graphing a Linear Inequality
1. Graph the boundary line Ax + By = C. \\ 2. Use a solid line for \leq or \geq. Use a dashed line for < or >. \\ 3. Test a point (like (0,0)) not on the line. \\ 4. If the test point satisfies the inequality, shade that side of the line. If not, shade the other side.
This four-step process is used to visually represent one constraint on the coordinate pl...
4 more steps in this tutorial
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Challenging
You have $10. Bags of chips (x) cost $2 each, and candy bars (y) cost $1.25 each. You must buy at least 4 items in total. What is the complete set of all possible integer purchase combinations?
A.(3,2), (2,4), (1,6), (0,8)
B.(4,0), (4,1), (3,2), (3,3), (2,4), (1,5), (1,6), (0,4), (0,5), (0,6), (0,7), (0,8)
C.(5,0), (4,1), (3,3), (2,4), (1,6), (0,8)
D.(4,0), (3,2), (2,4), (1,6), (0,8)
Challenging
A purchasing scenario is defined by the system 3x + 2y ≤ 10, x ≥ 1, y ≥ 1. If the budget is decreased from $10 to $8, how does the feasible region change?
A.It shrinks, because the boundary line 3x + 2y = 10 shifts inward to 3x + 2y = 8.
B.It expands, because the boundary line 3x + 2y = 10 shifts outward.
C.It shifts to the right, because the constraint x ≥ 1 changes.
D.It does not change, only the possible integer solutions change.
Challenging
You have exactly $10 to spend on muffins (x) at $2.50 each and croissants (y) at $1.25 each. You must buy more muffins than croissants. What is the only possible combination of items you can buy?
A.(4 muffins, 0 croissants)
B.(2 muffins, 4 croissants)
C.(1 muffin, 6 croissants)
D.(3 muffins, 2 croissants)
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Purchases - do you have enough money - up to $10 is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Purchases - do you have enough money - up to $10?
You'll be able to: Solve word problems to find the total cost of up to three items, each costing less than $10, with 80% accuracy; Determine if they have enough money (up to $10) to purchase a set of items by comparing the total cost to the amount….
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This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.