Topic Details (Notes format)

How to Approach Algebraic Word Problems

Subject: Mathematics

Book: Maths Mastery

Algebraic word problems typically revolve around forming one or more equations based on a scenario. The steps: define variables, translate sentences into expressions, and solve systematically. For example: “A number is 5 less than twice another. If the sum is 23, find the numbers.” Let x be the first number, y the second. Then x = 2y – 5, x + y = 23. Solve to get y=14, x=23–14=9. Understanding how to parse language into algebraic form is pivotal in advanced mathematics, finance, or logical puzzles, turning everyday challenges into solvable equations.

Practice Questions

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

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If 3x = 81, what is the value of x?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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

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A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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