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.
Answers
Answer:
Step-by-step explanation:
Let the age of daughter now be x
Before 7 years
Age of daughter = x-7
Age of father = 7×her age before 7 years
= 7(x-7)
= 7x-49
After 3 years
Age of daughter = x+3
Age of father = 3(x+3)
= 3x-9
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