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

A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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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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If 2x = 16, what is the value of x?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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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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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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If 5x - 2 = 13, what is the value of x?

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

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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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