Q. 14.0( 513 Votes )

# 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.

Given: Seven years ago, Aftab was seven times as old as his daughter and after 3 years Aftab will be 3 times as old as his daughter.
To Represent the situations algebraically and graphically we need to find the linear equations for these situations.
Let present age of Aftab = x

Let present age of his daughter = y

Then, seven years ago the age of Aftab and his daughter must have been seven less than their present ages,
Age of Aftab seven years ago = x – 7

Age of Daughter seven years ago = y – 7

According to the question,

Seven years ago, Aftab was seven times as old as his daughter, So

x - 7 = 7(y - 7)

⇒ x - 7 = 7y - 49

⇒ x = 7y - 42

Now for finding different points of this equation, we can either take different values of x and put them in the equation to obtain values of y or vice versa

Putting y = 5, 6 and 7 in equation (¡),

we get,
For y = 5,

x = 7 × 5 – 42
= 35 – 42
= -7
For x =6,

x = 7 × 6 – 42
= 42 – 42
= 0
For y = 7,

x = 7 × 7 – 42
= 49 – 42
= 7

Thus we got 3 points to plot on graph for this equation.
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 + 6

Now for finding different points of this equation, we can either take different values of x and put them in equation to obtain values of y or vice versa

Putting  x = 0, 3 and 6

Thus we got 3 points to plot on graph for this equation.
Algebraic representation

x - 7y = -42  (i)

x - 3y = 6     (ii)

Graphical representation:

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