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.” Is not this interesting? Represent this situation algebraically and graphically.

Answer 1

Let the present age of Aftab and his daughter be x and y respectively. 

Hence, seven years ago, 

Age of Aftab = x – 7 and Age of his daughter = y – 7 

According to the given condition, 

x – 7 = 7 (y – 7) 

⇒ x – 7y = -42……… (i) 

Three years from the present age, 

x + 3 = 3 (y + 3) 

⇒x – 3y = 6………..(ii) 

Therefore, equations (i) and (ii) represents the situation algebraically. To represent these equations graphically we need at least two solutions for each (i) and (ii). 

And let’s put them in a table for each: 

For equation (i),

x	-7	0	7
\(y = \frac{(x-6)}{3}\)	0	-1	-2

For equation (ii),

x	6	3	0
\(y = \frac{(x – 6)}{3}\)	0	-1	-2

The above can be plotted in a graph as below: