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

If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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If the probability of an event is 1/4, what is the probability of its complement?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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What is the greatest common divisor (GCD) of 36 and 48?

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The area of an equilateral triangle with side length 6 cm is:

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What is the HCF of 48 and 180?

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If x^2 + 4x + 4 = 0, what is the value of x?

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What is the square root of 144?

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The LCM of 12 and 15 is:

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