M.TMS.13
Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Example Problems
Aaron has $30 to spend on chocolate bars and lollipops. He buys a box of lollipops for $4.
After buying the lollipops, he wants to spend the remaining money on chocolate bars that cost $2.75 each.
Write and solve an inequality to find the greatest number of chocolate bars that Aaron can buy.
After buying the lollipops, he wants to spend the remaining money on chocolate bars that cost $2.75 each.
Write and solve an inequality to find the greatest number of chocolate bars that Aaron can buy.
Lionel goes to an office supply store with $45 to buy a mechanical pencil that costs $4.60. With the remaining money, he plans to buy as many pens as possible. Each pen costs $1.70.
Let represent the number of pens Lionel can buy.
Write and solve an inequality to find the maximum number of pens that Lionel can buy.
Let represent the number of pens Lionel can buy.
Write and solve an inequality to find the maximum number of pens that Lionel can buy.
Gabriella runs a catering business that charges a one-time setup fee of $50 plus $20 per guest. She wants each customer to pay at least $450 in total for an event.
Let represent the number of guests.
Write and solve an inequality to find the number of guests Gabriella needs to ensure that the charge is $450 or more.
Let represent the number of guests.
Write and solve an inequality to find the number of guests Gabriella needs to ensure that the charge is $450 or more.
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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