SOLUTION: Five years ago, Jacob was one sixth the age of his brother. In three years' time his age doubled will match his brother's age. How old is Jacob now? I know the answer is 7, but

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Five years ago, Jacob was one sixth the age of his brother. In three years' time his age doubled will match his brother's age. How old is Jacob now? I know the answer is 7, but       Log On


   

Question 825211: Five years ago, Jacob was one sixth the age of his brother. In three years' time his age doubled will match his brother's age. How old is Jacob now?
I know the answer is 7, but I'm not sure of the steps involved in getting it.
Thanks :)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +j+ = Jacob's age now
Let +b+ = brother's age now
+j+-+5+ = Jacob's age 5 years ago
+b+-+5+ = brother's age 5 years ago
+j+%2B+3+ = Jacob's age in 3 years
+b+%2B+3+ = brother's age in 3 years
---------------------------------
(1) +j+-+5+=+%281%2F6%29%2A%28+b+-+5+%29+
(2) +2%2A%28+j%2B3+%29+=+b+%2B+3+
-----------------------
(1) +6%2A%28+j-5+%29+=+b+-+5+
(1) +6j+-+30+=+b+-+5+
(1) +6j+-+b+=+25+
and
(2) +2j+%2B+6+=+b+%2B+3+
(2) +2j+-+b+=+-3+
------------------
Subtract (2) from (1)
(1) +6j+-+b+=+25+
(2) +-2j+%2B+b+=+3+
+4j+=+28+
+j+=+7+
Jacob is 7 now
check:
(1) +j+-+5+=+%281%2F6%29%2A%28+b+-+5+%29+
(1) +7+-+5+=+%281%2F6%29%2A%28+b+-+5+%29+
(1) +2+=+%281%2F6%29%2A%28+b-5+%29+
(1) +12+=+b+-+5+
(1) +b+=+17+
and
(2) +2%2A%28+j%2B3+%29+=+b+%2B+3+
(2) +2%2A%28+7%2B3+%29+=+17+%2B+3+
(2) +2%2A10+=+20+
(2) +20+=+20+
OK