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 rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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

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What is the remainder when 5^100 is divided by 3?

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If two complementary angles differ by 30°, what are the angles?

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A sphere has a radius of 7 cm. What is its volume?

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What is the value of x if log(x) + log(4) = log(32)?

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What is the area of an equilateral triangle with side length 10 cm?

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What is the sum of all even numbers between 1 and 50?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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