Topic Details (Notes format)

How to Solve Multi-Variable Word Problems (Systems of Equations)

Subject: Mathematics

Book: Maths Mastery

Realistic situations often require multiple unknowns: e.g., “Jake bought 2 apples and 3 bananas for ₹50, while Nina bought 4 apples and 1 banana for ₹40. Find each fruit’s cost.” Form equations from each statement: 2a+3b=50, 4a+b=40. Solve simultaneously (by substitution or elimination) to get a=10, b=10 in this example. These tasks arise in budgeting, mixture, or scheduling. Mastering multi-variable setups fosters robust problem-solving for real-life constraints that can’t be reduced to a single equation, bridging arithmetic to more advanced algebraic planning.

Practice Questions

How many ways can 4 people sit in a row?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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What is the LCM of 15 and 20?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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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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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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