**Word Problems: Linear Equations in One Variable - Class 8 Math**

Word problems involving linear equations in one variable are commonly encountered in various real-life situations. These problems require us to translate the given information into a mathematical equation and then solve it to find the unknown variable.

**Example 1:**
A shopkeeper sells 40 chairs at a price of $100 each. If he wants to increase the price by $20 per chair, how much money will he collect by selling all the chairs?

**Solution:**
Let's assume the increased price per chair is $x.

According to the given information:
Number of chairs sold = 40
Original price = $100
Increased price = $100 + $20 = $120

To find the total money collected, we need to multiply the number of chairs by the increased price:

Total money collected = Number of chairs × Increased price
Total money collected = 40 × $120
Total money collected = $4800

Therefore, the shopkeeper will collect $4800 by selling all the chairs.

**Example 2:**
The sum of two consecutive numbers is 57. Find the numbers.

**Solution:**
Let's assume the first number as 'x'.

According to the given information:
First number = x
Second number = x + 1 (as they are consecutive)

The sum of the two numbers is given as 57:

x + (x + 1) = 57

To solve this equation, we can simplify it:

2x + 1 = 57

Subtracting 1 from both sides:

2x = 56

Dividing both sides by 2:

x = 28

Therefore, the first number is 28, and the second number is 28 + 1 = 29.

**Example 3:**
The ages of two friends are in the ratio 5:7. If the sum of their ages is 48 years, find their ages.

**Solution:**
Let's assume the common ratio between their ages as 'x'.

According to the given information:
First friend's age = 5x
Second friend's age = 7x

The sum of their ages is given as 48 years:

5x + 7x = 48

Combining like terms:

12x = 48

Dividing both sides by 12:

x = 4

Substituting the value of 'x' back into the equations:

First friend's age = 5x = 5(4) = 20 years
Second friend's age = 7x = 7(4) = 28 years

Therefore, the ages of the two friends are 20 years and 28 years.

These examples demonstrate how word problems involving linear equations in one variable can be solved by translating the given information into equations and then solving them. Practice with more problems from your NCERT textbook to strengthen your understanding of this concept.

Chapter 2 exercise 2.2 question no. 17 (ii) please solve