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 .

Answer 1

Let present age of Aftab be $x$

And, present age of daughter is represented by $y$

$\text{Then Seven years ago,}$

Age of Aftab $=x-7$

Age of daughter $=y-7$

According to the question,

$(x-7)=7(y–7)$

$x–7=7y–49$

$x-7y=-49+7$

$x–7y=-42$…(i)

$x=7y–42$

$\text{Three years from now ,}$

Age of Aftab $=x+3$

Age of daughter $=y+3$

According to the question,

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

$x+3=3y+9$

$x-3y=9-3$

$x-3y=6$ …(ii)

$x=3y+6$

$\text{Algebraic representation}$

From equation (i) and (ii)

$x–7y=–42$ …(i)

$x-3y=6$ …(ii)