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→ Mary told her 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". Find the present age of Mary and her daughter .......
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Answers
The answer is in the attachment.....
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Let the present age of Mary is 'x' and her daughter age is 'y'.
7 years ago:
Age of Mary = x - 7.
Age of Daughter = y - 7.
Given that I(Mary) was seven times as old as you(Daughter) were then.
⇒ x - 7= 7(y - 7)
⇒ x - 7 = 7y - 49
⇒ x - 7y + 42 = 0
⇒ x - 7y = -42 ------ (1)
3 years hence:
Age of Mary = x + 3.
Age of daughter = y + 3.
Given that I shall be three times as old as you will be.
⇒ x + 3 = 3(y + 3)
⇒ x + 3 = 3y + 9
⇒ x - 3y = 6 ------- (2)
On solving (1) & (2), we get
⇒ x - 7y = -42
⇒ x - 3y = 6
------------------
-4y = -48
y = 12.
Substitute y = 12 in (1), we get
⇒ x - 7y = -42
⇒ x - 7(12) = -42
⇒ x - 84 = -42
⇒ x = -42 + 84
⇒ x = 42.
Therefore,
∴ Present age of Mary = 42 years.
∴ Present age of her daughter = 12 years.
Hope this helps!