Topic Details (Notes format)

How to Solve Systems of Inequalities Word Problems

Subject: Mathematics

Book: Maths Mastery

Many real-world constraints call for multiple inequalities, like “Work hours ≤ 40, wage/hour ≥ ₹100, and total weekly pay ≥ ₹3,500.” Represent each constraint as an inequality, then find the feasible region if you have two or more variables. For instance, x≥100, y≤40, and xy≥3,500 in some context. Graphing or systematically analyzing these inequalities reveals possible solutions. Industrial engineering, resource allocation, or scheduling tasks rely heavily on systems of inequalities for optimization. Mastering them fosters an ability to handle advanced planning with multiple constraints or objectives.

Practice Questions

The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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If the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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What is the square root of 0.25?

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The probability of rolling a sum of 7 with two dice is:

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A cube has a side length of 4 cm. What is its volume?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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