SOLUTION: The sum of Bill's and Ted's age is 34 years. Five years ago the sum of twice Bill's and three times Ted's age was 59 years. How old are they now?

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Question 563244: The sum of Bill's and Ted's age is 34 years. Five years ago the sum of twice Bill's and three times Ted's age was 59 years. How old are they now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = Bill's age now
Let +t+ = Ted's age now
given:
(1) +b+%2B+t+=+34+
(2) +2%2A%28+b+-+5+%29+%2B+3%2A%28+t+-+5+%29+=+59+
----------------------------
(2) +2b+-+10+%2B+3t+-+15+=+59+
(2) +2b+%2B+3t+=+59+%2B+25+
(2) +2b+%2B+3t+=+84+
Multiply both sides of (1) by 2, and
subtract (1) from (2)
(2) +2b+%2B+3t+=+84+
(1) +-2b+-+2t+=+-68+
+t+=+16++
and
(1) +b+%2B+t+=+34+
(1) +b+%2B+16+=+34+
(1) +b+=+34+-+16+
(1) +b+=+18+
Bill is 18 and Ted is 16
check:
(2) +2%2A%28+b+-+5+%29+%2B+3%2A%28+t+-+5+%29+=+59+
(2) +2%2A%28+18+-+5+%29+%2B+3%2A%28+16+-+5+%29+=+59+
(2) +2%2A13+%2B+3%2A11+=+59+
(2) +26+%2B+33+=+59+
(2) +59+=+59+