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 the present age of aftab be x years and let the present age of her daughter be y years .

according to first condition,

aftab 's age was (x-7) years and

his daughter 's age was (y-7) years.

so, x-7 = 7(y-7)

x-7 = 7y- 49

x-7y = -49 + 7

x-7y = -42 ...... i eq.

according to second condition,

aftab 's age will be (x+3) years and

her daughter 's age will be (y+3) years

so, x+3 = 3(y+3)

x+3 = 3y + 9

x-3y = 9-3

x-3y = 6 ......ii eq.

( REPRESENT IT GRAPHICALLY BY YOURSELF)

Answer 2

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