SOLUTION: The sum of a man's age and his grandmother's age is 102. Eighteen years age his grandmother was 10 times as old as he was then. Find their present ages.

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Question 474228: The sum of a man's age and his grandmother's age is 102. Eighteen years age his grandmother was 10 times as old as he was then. Find their present ages.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = Man's present age
Let b = Grandmother's present age
+a+-+18+ = Man's age 18 years ago
+b+-+18+ = Gradmother's age 18 years ago
given:
(1) +a+%2B+b+=+102+
(2) +b+-+18+=+10%2A%28a+-+18%29+
------------------------
(2) +b+-+18+=+10a+-+180+
(2) +10a+-+b+=+180+-+18+
(2) +10a+-+b+=+162+
Add (2) to (1)
(2) +10a+-+b+=+162+
(1) +a+%2B+b+=+102+
+11a+=+264+
+a+=+24+
And, from (1),
+a+%2B+b+=+102+
+24+%2B+b+=+102+
+b+=+78+
The man is 24 and the Grandmother is 78
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check:
(2) +b+-+18+=+10%2A%28a+-+18%29+
(2) +78+-+18+=+10%2A%2824+-+18%29+
(2) +60+=+60+
OK