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

What is the sum of all odd numbers from 1 to 99?

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What is the sum of the first 50 positive integers?

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If x^2 + 4x + 4 = 0, what is the value of x?

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A car travels 240 km in 4 hours. What is its average speed?

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If the perimeter of a square is 40 cm, what is the area of the square?

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If the sum of three consecutive integers is 72, what are the integers?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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