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

A number is increased by 20% and then decreased by 10%. What is the net change?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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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 probability of drawing a king from a standard deck of 52 playing cards?

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

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What is the HCF of 72 and 120?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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The LCM of 12 and 15 is:

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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