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

What is the sum of all even numbers between 1 and 100?

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What is the square root of 121?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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

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

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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

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What is the HCF of 72 and 120?

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If a person can type 45 words per minute, how many words can they type in 2 hours?

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If 2x - 3 = 7, what is the value of x?

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