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

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What is the sum of the first 10 positive even numbers?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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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 cube root of 729?

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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The probability of rolling a sum of 7 with two dice is:

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

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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