NC.M3.A-CED.3
Create systems of equations and/or inequalities to model situations in context.
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 ResourcesLogarithm change of base rule introSolving exponential equations using logarithmsUsing units to solve problemsExponential model word problemsSolve exponential equations using logarithms: base-2 and other basesSolve exponential equations using logarithms: base-10 and base-eUsing inequalities to solve problemsTwo-variable inequalities word problemsSystems of equations word problems (with zero and infinite solutions)Evaluate logarithms: change of base ruleComparing linear rates word problemsConstruct exponential modelsModeling with sinusoidal functionsSystems of inequalities word problemsSystems of equations with substitution: potato chipsQuadratic equations word problem: triangle dimensionsUsing units to solve problems: Drug dosageModeling with systems of inequalitiesQuadratic equations word problem: box dimensionsEvaluating logarithms: change of base ruleConstructing exponential models: percent changeTrig word problem: modeling annual temperatureConstructing exponential models: half lifeSolving exponential equations using logarithms: base-10Exponential model word problem: bacteria growthGraphs of systems of inequalities word problemExponential model word problem: medication dissolveComparing linear rates exampleWriting systems of inequalities word problemTwo-variable linear equations introSolving exponential equations using logarithms: base-2Solving two-variable inequalities word problemConstructing exponential modelsSolving systems of inequalities word problemTrig word problem: modeling daily temperatureUsing inequalities to solve problems

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