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)
| x | 0 | 6 | 14 |
| y = \(x + 42\over 7\) | 6 | 7 | 8 |
| Points | A | B | C |
For x – 3y = 6
| x | 6 | 12 | 18 |
| y = \(x – 6\over 3\) | 0 | 2 | 4 |
| Points | D | E | F |
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.
