SOLUTION: The sum of the ages of a boy and his father is 60 years. Six years ago the boy's age was one-seventh of what his father's was. What are their ages now?

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Question 1064577: The sum of the ages of a boy and his father is 60 years. Six years ago the boy's age was one-seventh of what his father's was. What are their ages now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the son's age now
Let +b+ = the father's age now
---------------------------------
(1) +a+%2B+b+=+60+
(2) +a+-+6+=+%281%2F7%29%2A%28+b+-+6+%29+
---------------------------------
(2) +7%2A%28+a+-+6+%29+=+b+-+6+
(2) +7a+-+42+=+b+-+6+
(2) +7a+-+b+=+36+
----------------------------
Add (1) and (2)
(1) +a+%2B+b+=+60+
(2) +7a+-+b+=+36+
------------------------
+8a+=+96+
+a+=+12+
and
(1) +a+%2B+b+=+60+
(1) +b+=+60+-+12+
(1) +b+=+48+
-----------------------
The son is 12
The father is 48
--------------------
(2) +a+-+6+=+%281%2F7%29%2A%28+b+-+6+%29+
(2) +12+-+6+=+%281%2F7%29%2A%28+48+-+6+%29+
(2) +6%2A7+=+42+
(2) +42+=+42+
OK