Answer:

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.

Ans. Let the present age of Aftab = x

And, present age of his daughter is represented as = y

Seven years ago,

Aftab’s age = x – 7

Age of Aftab’s daughter = y – 7

According to the question,

(x – 7) = 7 (y – 7 )

x – 7 = 7 y – 49

x – 7y = – 49 + 7

x – 7y = – 42 … (i)

x = 7y – 42

Putting y = 5, 6 and 7, we get

x = 7 × 5 – 42 = 35 – 42 = – 7

x = 7 × 6 – 42 = 42 – 42 = 0

x = 7 × 7 – 42 = 49 – 42 = 7

Three years from now,

Aftab’s age = x + 3

Age of Aftab’s 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

Putting, y = – 2, –1 and 0, we get

x = 3 × – 2 + 6 = – 6 + 6 =0

x = 3 × – 1 + 6 = – 3 + 6 = 3

x = 3 × 0 + 6 = 0 + 6 = 6

Algebraic representation

From equation (i) and (ii)

x – 7y = – 42 … (i)

x – 3y = 6 … (ii)

Graphical representation