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Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Solution:

Assume the present age of Aftab be x years and his daughter be y years. 

Present age of Aftab = x years and his daughter = y years

Therefore, 7 years ago, age of Aftab = (x - 7) years and his daughter = (y - 7) years

Using this information and applying the known condition that 7 years ago, Aftab was 7 times as old as his daughter then:

x - 7 = 7(y - 7)

x - 7 = 7y - 49

x - 7y - 7 + 49 = 0

x - 7y + 42 = 0

After 3 years from now, age of Aftab = (x + 3) years and his daughter's age = (y + 3) years

Also, Aftab will be 3 times as old as his daughter which can be represented as:

x + 3 = 3 (y + 3)

x + 3 = 3y + 9

x - 3y + 3 - 9 = 0

x - 3y - 6 = 0

Thus we have,

x - 7y + 42 = 0 ----(1)

x - 3y - 6 = 0 ----(2)

Therefore, the algebraic representation is for equation (1) is:

x - 7y + 42 = 0

-7y = - x - 42

7y = x + 42

y = (x + 42)/7

And, algebraic representation for equation (2) is:

x - 3y - 6 = 0

- 3y = - x + 6

3y = x - 6

y = (x - 6)/3

Let us represent these equations graphically. For this, we need at least two solutions for each equation. Let's tabulate the solutions.

For equation (1), 

x

21

28

y = (x + 42)/7

9

10

For equation (2),

x

30

21

y = (x - 6)/3

8

5

The graphical representation is as follows.

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

x axis:1 unit = 10 years, y axis: 1 unit = 2 years

The present age of Aftab is 42 years and his daughter is 12 years old.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 3

Video Solution:

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

NCERT Solutions Class 10 Maths Chapter 3 Exercise 3.1 Question 1

Summary:

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” This situation is algebraically and graphically represented. Aftab is 42 years old and his daughter is 12 years old at present.

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