Question 176617: father say to his son seven years ago i was 7 times as old as you were but 3 years hence my age will be twice that of yours .find their ages?
Answer by MathTherapy(10559)   (Show Source):
You can put this solution on YOUR website! Hence means “from now.”
Let s = son’s age now
Then 7 years ago, son’s age was s - 7
Since father’s age, 7 years ago was 7 times his son’s, then father’s age then was 7(s – 7) = 7s - 49
In 3 years time, son’s and father’s ages would be their ages 7 years ago, plus 10 years
Therefore, their ages, 3 years from now, or 10 years from 7 years ago will be s – 7 + 10, or s + 3 (son’s), and 7s – 49 + 10, or 7s – 39 (father’s).
Now, since in 3 year’s time, the father’s age will be twice that of his son’s, then we have: 2(s + 3) = 7s – 39
2s + 6 = 7s – 39
-5s = - 45
s = 9
Therefore, son is now 9 years-old.
Now, since 7 years ago, father’s age was 7 times his son’s, then 7 years ago, his son was (9 – 7) = 2, which means that the father was 7(2), or 14 years-old then.
If father was 14 years old 7 years ago, that makes him 21 years-old now.
Checking to see if this is correct, let’s calculate their ages 3 years from now. 3 years from now, the son will we 12 (9 + 3), and the father will be 24 (21 + 3). This shows that in 3 year’s time, the father, at 24, will be twice the son’s age of 12.
Therefore, the son is now 9 years old, and the father is 21 years-old.
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