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 man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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What is the sum of the first 50 positive integers?

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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 x² - 9x + 18 = 0, what are the roots of the equation?

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

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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What is the LCM of 15 and 20?

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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If 3x = 81, what is the value of x?

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