Rajesh says to 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". If we choose the present age of Rajesh and his daughter be 'x' and 'y' . Which of the following pair of equations represent this situation algebraically.
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Given:
Seven years ago Rajesh was seven times as old as his daughter then.
Three years from now, he will be three times as old as his daughter will be.
To Find:
The pair of equations that represent this situation algebraically.
Solution:
- Let the present age of Rajesh be x and the present age of his daughter be y.
- According to question:
(x - 7) = 7 (y - 7)
⇒ x - 7 = 7y - 49
⇒ x - 7y + 42 = 0 ....(i)
- Also:
(x + 3) = 3 (y + 3)
⇒ x + 3 = 3y + 9
⇒ x - 3y - 6 = 0 ....(ii)
- So, the pair of equations to represent the given situation algebraically are:
x - 7y + 42 = 0
x - 3y - 6 = 0
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