NCERT Solutions Class 8 Maths Chapter 2 Exercise 2.2
Welcome back, future mathematicians! Today we are diving deep into linear equation ex 2 2 class 8 ncert, which focuses entirely on applying linear equations in one variable to solve real-world word problems. Word problems can often look intimidating, but they are simply puzzles waiting to be unraveled. In Exercise 2.2, we learn how to translate regular English statements—like finding unknown numbers, calculating relative ages, finding perimeters of shapes, or counting money—into mathematical expressions. Once you successfully build your equation, finding the correct solution is a breeze! Let us conquer these word problems together with step-by-step solutions and handy tricks from your YoLearn AI Tutor.
Understanding the Language of Word Problems
To solve any word problem in class 8 maths linear equation ex 2 2, you need to think like a translator. Think of algebra as a new language. Words like 'is', 'gives', or 'results in' convert directly into the equals sign (=). Words like 'sum', 'increased by', or 'added to' signify addition (+). Conversely, terms like 'difference' or 'subtracted from' point to subtraction (-), and 'times' or 'product' indicate multiplication. Always start by identifying what you do not know. This unknown quantity is assigned a variable, usually $x$. Once you have your variable, use the clues in the question to write expressions for the other terms, and then link them together to construct your final balanced linear equation.
Step-by-Step Blueprint to Solve Ex 2.2 Problems
- Identify the Key Unknown — Carefully read the question to find what you need to calculate. Assign a variable like $x$ to this base unknown quantity.
- Express Other Quantities — Translate relationships from the text to write expressions for other unknown values in terms of your variable $x$.
- Set Up the Balanced Equation — Formulate a mathematical equation by connecting your expressions with the key conditional statements given in the word problem.
- Solve and Isolate the Variable — Simplify the equation using arithmetic rules, keeping the variable on one side and constants on the other to solve for $x$.
- Verify and Finalize — Check if your calculated values fit the conditions of the original question, then state your final answers with correct units.
Typical Solved Examples from Exercise 2.2
- Example 1 (Consecutive Integers): The sum of three consecutive integers is 51. Find these integers. Step 1: Let the three consecutive integers be $x$, $x+1$, and $x+2$. Step 2: Set up the equation: $x + (x+1) + (x+2) = 51$. Step 3: Simplify the left side: $3x + 3 = 51$. Step 4: Subtract 3 from both sides: $3x = 48$. Step 5: Divide by 3: $x = 16$. Step 6: Find the consecutive integers: $x = 16$, $x+1 = 17$, $x+2 = 18$. Thus, the integers are 16, 17, and 18.
- Example 2 (Age-based Problem): A mother's age is 3 times her son's age. After 5 years, the sum of their ages will be 66 years. Find their present ages. Step 1: Let the son's present age be $x$ years. The mother's present age is $3x$ years. Step 2: After 5 years, Son's age = $x + 5$, Mother's age = $3x + 5$. Step 3: Sum of their ages after 5 years = $(x+5) + (3x+5) = 66$. Step 4: Simplify: $4x + 10 = 66 \implies 4x = 56 \implies x = 14$. Thus, the son is 14 years old and the mother is 42 years old.
Watch Out for the 'Subtracted From' Trap!
A common mistake students make is with subtraction translation. For example, '5 subtracted from a number $x