Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 → Algebra → Linear Equations in One Variable ↓


Word Problems on Linear Equations


When learning about linear equations, a common task is to solve word problems. Word problems require us to convert words into a mathematical equation that can be solved using linear equations. The skill of translating these real-world scenarios into mathematical expressions is important for understanding and solving problems in a variety of contexts.

Introduction to linear equations

A linear equation in one variable is an equation that can be written in the following form:

ax + b = 0

Here, a and b are constants and x is the variable. The objective is to find the value of x that makes the equation true.

Understanding word problems in linear equations

A word problem presents a situation in narrative form. It can describe a real-life scenario with various unknowns and relationships, which you need to interpret and express as a linear equation.

Steps to solve word problems

  1. Read the problem carefully and understand what is being asked.
  2. Identify the unknown(s) and assign a variable to represent the unknown.
  3. Translate the terms into an algebraic equation using variables.
  4. Solve the equation for the unknown variable.
  5. Check your solution by substituting it into the original terms of the problem.
  6. Write a complete sentence that answers the question posed by the problem.

Examples of word problems

Example 1: Simple number problem

The sum of a number and 7 is 15. What is that number?

Let us solve this step by step.

  1. Identify the unknown: number.
  2. Let's assign it a variable: x.
  3. Translate the terms into an algebraic equation:
    x + 7 = 15
  4. Solve the equation:
    x + 7 = 15 x = 15 - 7 x = 8
  5. The number is 8.

Example 2: Age problem

John is 4 years older than Jane. If the sum of their ages is 20, how old is each of them?

Step-by-step solution:

  1. Determine the variables: Let x be Jane's age. Then, John's age will be x + 4.
  2. According to the problem, the sum of their ages is 20:
    x + (x + 4) = 20
  3. Simplify and solve:
    2x + 4 = 20 2x = 20 - 4 2x = 16 x = 16 / 2 x = 8
  4. So, Jane is 8, and John is 8 + 4 = 12.

Example 3: Price of goods

Sarah bought 5 books and a pen. The total cost was $35. Each book cost $6. How much did the pen cost?

  1. Specify a variable for the unknown. Let p be the price of the pen.
  2. Write the equation for total cost:
    5 * 6 + p = 35
  3. Simplify and solve:
    30 + p = 35 p = 35 - 30 p = 5
  4. The pen cost $5.

Visual example: Solving word problems

Visualizing how word problem translation works can help us understand these problems in terms of interpretation.

word problem Explore the unknown Translate into an equation Solve the equation

Example 4: Distance and rate problem

A car travels at a speed of 60 km/h. How much distance will it cover in 3 hours?

  1. Understand the problem: you need to find the distance traveled, for which the formula is usually used:
    Distance = Speed * Time
  2. Substitute the known values into the formula:
    Distance = 60 * 3
  3. Solve:
    Distance = 180
  4. Therefore, the car travels 180 kilometres.

Strategies for dealing with complex problems

Here are some strategies for complex word problems:

  • Break the problem down into smaller, manageable parts.
  • Draw pictures or charts to show relationships.
  • Use the process of elimination - solve for a variable and substitute it into the other equations if multiple unknowns are involved.
  • Double-check the calculations by re-entering the values in the original problem statement.

Practice problems

Now solve these questions to test your understanding.

Problem 1

Tom has twice as many apples as Jerry. If they have 18 apples in total, how many apples will each person have?

Problem 2

A tank contains 150 liters of water. If the water flows out at the rate of 15 liters per minute, how long will it take to fill the tank?

Problem 3

If on subtracting 11 from three times a number we get 22, then find the number.

Problem 4

The perimeter of a rectangular garden is 48 m. If the length is twice the width, find the dimensions of the garden.

Review and conclusion

Solving word problems using linear equations may seem challenging initially, but with practice, you can improve your skills significantly. It is important to understand the problem well and convert it into an equation accurately. With systematic practice and careful thought process, you can become adept at solving a variety of real-world problems efficiently.


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Word Problems on Linear Equations

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