**Word Problems Involving Linear Equations in Two Variables :**

In this section, we will learn, how to solve word problems using linear equations with two variables.

**Example 1 :**

Raman’s age is three times he sum of the ages of his two sons. After 5 years his age will be twice the sum of the ages of his two sons. Find the age of Raman

**Solution :**

Let x be Raman's age and y be the sum of ages of his two sons.

x = 3y -----(1)

After 5 years :

Raman's age = x + 5

The sum of the ages of his two sons = y + 5 + 5

= y + 10

x + 5 = 2(y + 10)

x + 5 = 2y + 20

x - 2y = 20 - 5

x - 2y = 15 --------(2)

By applying the value of x in (2), we get

3y - 2y = 15

y = 15

x = 3(15)

x = 45

Hence, Raman is 45 years old.

**Example 2 :**

The middle digit of a number between 100 and 1000 is zero and the sum of the other digit is 13. If the digits are reversed, the number so formed exceeds the original number by 495. Find the number

**Solution :**

The required number will be in the form X 0 Y

Middle digit = 0

x + y = 13 -------(1)

Y 0 X = X0Y + 495

100y + x = 100x + 1y + 495

x - 100x + 100y - y = 495

-99x + 99y = 495

-x + y = 5 -------(2)

x = y - 5

By applying the value of x in (1), we get

y - 5 + y = 13

2y = 13+5

2y = 18

y = 9

When y = 9,

x = 9 - 5

x = 4

Hence, the required number is 409.

After having gone through the stuff given above, we hope that the students would have understood, how to solve word problems using linear equations with two variables.

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