Systems of Inequalities Word Problems

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What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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How do you represent a word problem as a system of inequalities?

Back

Identify the variables, determine the constraints (inequalities), and express the objective (goal) as an inequality.

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What does the inequality 2x + 3y > 100 represent in a word problem context?

Back

It represents a condition where the total value of items (e.g., bracelets and earrings) sold must exceed $100.

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What does the inequality x + y ≤ 40 signify in a jewelry-making scenario?

Back

It signifies that the total number of jewelry pieces made (bracelets and earrings) cannot exceed 40.

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What is the significance of the inequality x + y < 10 in a basketball scoring problem?

Back

It indicates that the total number of shots taken (2-point and 3-point) must be less than 10.

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What does the inequality 2x + 3y ≥ 20 mean in the context of scoring points?

Back

It means that the total points scored from the shots must be at least 20.

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How do you interpret the inequality x + y ≤ 300 in a ticket-selling scenario?

Back

It indicates that the total number of tickets sold (for adults and children) cannot exceed the theater's seating capacity of 300.

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What does the inequality 7.5x + 5.5y ≥ 2000 represent in a movie theater context?

Back

It represents the requirement that the total revenue from ticket sales must be at least $2000.

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What does the inequality x + y ≤ 6 signify in a cookie-baking problem?

Back

It signifies that the total hours spent baking cookies cannot exceed 6 hours.

Front

What does the inequality 32x + 20y ≥ 150 mean in the context of baking cookies?

Back

It means that the total number of cookies baked must be at least 150.