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.

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.

Solution:

Let the present age of Aftab be ‘x’.
And, the present age of his daughter be ‘y’.
Now, we can write, 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 ………………………(i)

Also, three years from now or after three years,
Age of Aftab will become = x + 3.
Age of his daughter will become = y + 3
According to the situation given,
x+3 = 3(y+3)
⇒x+3 = 3y+9
⇒x−3y = 6 …………..…………………(ii)

Subtracting equation (i) from equation (ii) we have
(x−3y)−(x−7y) = 6−(−42)
⇒−3y+7y=6+42
⇒4y=48
⇒y=12

The algebraic equation is represented by
x−7y = −42
x−3y = 6
For, x−7y =−42 or x = −42+7y
The solution table is
For, x−3y=6 or x=6+3y
The solution table is
The graphical representation is: