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

The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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

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The LCM of 12 and 15 is:

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If x - y = 5 and x + y = 15, what is the value of x?

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If x^2 - 6x + 9 = 0, what is the value of x?

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

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

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

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If a number is divisible by 9, it is also divisible by which of the following?

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