Question

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

Answer 1

Let the present age of Aftab be x.

And, present age of his daughter = y

Seven years ago,

Age of Aftab = x − 7

Age of his daughter = y − 7

According to the question,

(x - 7) = 7(y - 7)

x - 7 = 7y - 49

x - 7y =  - 42 ... (1)

Three years hence,

Age of Aftab = x + 3

Age of his daughter = y + 3

According to the question,

(x + 3) = 3(y + 3)

(x+3) = 3y+9

x - 3y = 6 ..... (2)

Therefore, the algebraic representation is

x - 7y = -42

x - 3y = 6

For x -7y =  -42

x = -42 + 7y

The solution table is

x	− 7	0	7
y	5	6	7

For x-3y=6

Let the present age of Aftab be x.

And, present age of his daughter = y

Seven years ago,

Age of Aftab = x − 7

Age of his daughter = y − 7

According to the question,

(x - 7) = 7(y - 7)

x - 7 = 7y - 49

x - 7y =  - 42 ... (1)

Three years hence,

Age of Aftab = x + 3

Age of his daughter = y + 3

According to the question,

(x + 3) = 3(y + 3)

(x+3) = 3y+9

x - 3y = 6 ..... (2)

Therefore, the algebraic representation is

x - 7y = -42

x - 3y = 6

For x -7y =  -42

x = -42 + 7y

The solution table is

x	− 7	0	7
y	5	6	7

For x - 3y = 6

x = 6 + 3y

The solution table is

x	6	3	0
y	0	− 1	− 2

The graphical representation is as follows.