A-CED.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Example Problems
It takes 12 hours and $250 to paint a single-family home, and it takes 80 hours and $600 to paint a commercial building.
A painting company has less than $70000 to paint these properties, and it wants to spend at most 900 hours to do so.
Let denote the number of single-family homes they paint and the number of commercial buildings they paint.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
A painting company has less than $70000 to paint these properties, and it wants to spend at most 900 hours to do so.
Let denote the number of single-family homes they paint and the number of commercial buildings they paint.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
It takes 15 hours and $250 to build a bicycle, and it takes 100 hours and $300 to build a scooter.
A company has less than $80000 to build these products, and it wants to spend at most 500 hours to do so.
Let denote the number of bicycles they build and the number of scooters they build.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
A company has less than $80000 to build these products, and it wants to spend at most 500 hours to do so.
Let denote the number of bicycles they build and the number of scooters they build.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
It takes and to assemble a smartphone, and it takes and to assemble a tablet.
An electronics company has less than to assemble these devices, and it wants to spend at most to do so.
Let denote the number of smartphones they assemble and the number of tablets they assemble.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
An electronics company has less than to assemble these devices, and it wants to spend at most to do so.
Let denote the number of smartphones they assemble and the number of tablets they assemble.
Write a system of inequalities that represents the following conditions:
1. An inequality that represents the condition based on the number of dollars the company can spend.
2. An inequality that represents the condition based on the number of hours the company wants to spend.
Khan Academy ResourcesTwo-variable inequalities word problemsSystems of equations word problems (with zero and infinite solutions)Systems of inequalities word problemsSystems of equations with substitution: potato chipsModeling with systems of inequalitiesGraphs of systems of inequalities word problemWriting systems of inequalities word problemSolving two-variable inequalities word problemSolving systems of inequalities word problem

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