Word Problems on Linear Equations
Translating real-world scenarios into mathematical linear equations to find unknown values.
Definition
Word problems require translating real-life verbal statements into mathematical linear equations. This process involves identifying the unknown quantity, assigning a variable to it, framing an equation based on the given conditions, and solving it. Finally, the obtained mathematical solution must be interpreted in the context of the original problem.
Key formula
Total = Sum of parts / Rate * Time = Distance
Worked examples
If the sum of two consecutive numbers is 27, let the numbers be x and x + 1. The equation is x + x + 1 = 27, which gives 2x = 26, so x = 13 and the numbers are 13 and 14.
Bansi has 3 times as many two-rupee coins as five-rupee coins. If the total value is Rs. 77, let five-rupee coins be x, then two-rupee coins are 3x. Equation: 5x + 2(3x) = 77, leading to 11x = 77, so x = 7.
The perimeter of a rectangular swimming pool is 154m. Its length is 2m more than twice its breadth. Let breadth be x, length be 2x + 2. Equation: 2(length + breadth) = 154, yielding x = 25m and length = 52m.
Common mistakes
- • Failing to read the problem carefully, leading to incorrectly defined variables.
- • Forgetting to verify if the final answer makes logical sense in the context of the real-world scenario.
Introduction to Rational Numbers
Rational Numbers
Properties of Rational Numbers
Rational Numbers
Representation on Number Line
Rational Numbers
Rational Numbers Between Two Rational Numbers
Rational Numbers
Algebraic Expressions and Equations
Linear Equations in One Variable
Solving Equations with Variables on Both Sides
Linear Equations in One Variable