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

If 2a + b = 10 and a - b = 4, what is the value of a?

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If the radius of a circle is doubled, what happens to its area?

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

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

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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A number is increased by 20% and then decreased by 20%. What is the net change?

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

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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