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.”

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.

Solution : Let the present age of father be x years and the age of daughter be y years

Seven years ago fathers’s age = (x – 7) years

Seven years ago daughter’s age = (y – 7) years

According to problem,

(x – 7) = 7(y – 7)   or   x – 7y = -42                         ………….(1)

After three years father’s age = (x + 3) years

After three years daughter’s age = (y + 3) years

According to the condition given in the question,

(x +3) = 3(y + 3)     or     x – 3y =  6                    …………..(2)

For (x – 7y = -42)

x0614
y = \(x + 42\over 7\)678
PointsABC

For x – 3y = 6

x61218
y = \(x – 6\over 3\)024
PointsDEF

Plot the points A(0, 6), B(7, 7), C(4,8) and join them to get a straight line ABC. Similarly plot the points D(6, 0), E(12, 2) and F(18, 4) and join them to get a straight line DEF.

Graph

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