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

Answer:

Let Aftab's present age be x

Let daughter's present age be y

Age 7 years ago

Aftab's age = x-7

daughter's age = y-7

According to 1st statement

x -7 = 7(y-7)

x-7 = 7y -49

x-7y = -42

Age 3 years from now

Aftab's age = x+3

daughter's age = y +3

According to second statement

x + 3 = 3(y+3)

x+3 = 3y+9

x-3y = 6

Answer 2

ANSWER:-

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

   

$\mathtt{x - 7 = 7(y - 7)}$

$\mathtt{ \implies x - 7 = 7y - 49}$

$\mathtt{ \implies x - 7y = - 42} \: \: \: \: \: ...(1)$

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,

$\mathrm{(x - 3y) - (x - 7y) = 6 - ( - 42)}$

$\mathrm{\implies 3y + 7y = 6 + 42}$

$\mathrm {\implies 4y = 48}$

$\rm{\implies y = 12}$

The algebraic equation is represented by

x−7y = −42

x−3y = 6

For,  x−3y = 6   or     x = 6+3y