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

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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If a square has a perimeter of 64 cm, what is its area?

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What is the area of a circle with a diameter of 14 cm?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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What is the HCF of 48 and 180?

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If sin(A) = 1/2 and A is acute, what is the value of A?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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

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