SOLUTION: i am seven times as old as you were when i was as old as you are said a man to his son. If the sum of their present ages in years is 110 then what is their present age?

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Question 883776: i am seven times as old as you were when i was as old as you are said a man to his son. If the sum of their present ages in years is 110 then what is their present age?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the present age of the son
Let +b+ = the present age of the father
-------------------------------------
Note that the difference in their ages will
never change: it is +b+-+a+
----------------------------
The father says: " when I was as old as you are "
That means when the father's age was +a+
Back then, the son's age must have been:
+a+-+%28+b+-+a+%29+=+2a+-+b+
--------------------------
The father says " I am 7 times as old as you were
when I was as old as you are ", so
(1) +b+=+7%2A%28+2a+-+b+%29+
also given:
(2) +a+%2B+b+=+110+
---------------------
(1) +b+=+14a+-+7b+
(1) +14a+=+8b+
(1) +7a+=+4b+
(1) +a+=+%28+4%2F7+%29%2Ab+
By substitution:
(2) +%28+4%2F7+%29%2Ab+%2B+b+=+110+
(2) +%28+11%2F7+%29%2Ab+=+110+
(2) +%28+1%2F7+%29%2Ab+=+10+
(2) +b+=+70+
and, since
(2) +a+%2B+b+=+110+
(2) +a+=+40+
---------------
The father is 70 and the son is 40
check:
The difference +b-+a+=+30+
+a+-+%28+b+-+a+%29+=+40+-+30+
+40+-+30+=+10+
(1) +b+=+7%2A%28+2a+-+b+%29+
(1) +b+=+7%2A10+
(1) +b+=+70+
OK