Ravish tells his daughter Aarushi, “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”. If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically.
Solution
It is given that seven year ago Ravish was seven times as old as his daughter
∴ 7 ( x - y ) = y - 7
⇒ 7x - 49 = y -7
⇒ 7x - 42 = y ............. (1)
It is also given that after three years from now Ravish shall be three times a sold as her daughter
∴ 3 ( x + 3 ) = y + 3 ⇒ 3x + 9 = y + 3 ⇒ 3x + 6 = y ........... (2)
Now , y = 7x - 42 [ using (1) ]
Putting x = 6 , we get y = 7 × 6 - 42 = 0
Putting x = 5, we get y = 7 × 5 - 42 = - 7
Thus, we have following table for the points on the
Line 7x - 42 = y
| x | 6 | 5 |
| y | 0 | -7 |
We have,
y = 3x + 6 [ using (2) ]
Putting x = - 2 , we get y = 3 × ( -2 ) + 6 = 0
Putting x = -1 , we get y = 3× (-1) + 6 = 3
Thus, we have following table for the points on the
Line y = 3x + 6
| x | -1 | -2 |
| y | 3 | 0 |
