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 there times as old as you will be." Represent this situation algebraically.

Answer 1

Let Aftab's present age is '$x$' years and his daughter's is '$y$' years.

Case 1:

Seven years ago,

Aftab's age $=x-7$ years

His daughter $=y-7$.years.

Since, Aftab told to his daughter, "Seven years ago, I was seven times as old as you were then"

$\Rightarrow (x-7)=7(y-7)$

$\Rightarrow x-7=7y+49$

$\Rightarrow x-7y-7+49=0$

$\Rightarrow x-7y+42=0$ ---(1)

Case 2:

Three years from now,

Aftab's age $=x+3$ years

His daughter $=y+3$ years

Since, Aftab told to his daughter, "Three years from now, I shall be there times as old as you"

$\Rightarrow x+3=3(y+3)$

$\Rightarrow x+3=3y+9$

$\Rightarrow x+3-3y-9=0$

$\Rightarrow x-3y-6=0$ ---(2)

Hence, (1) and (2) represents the given problem algebraically.