SOLUTION: three years ago, joe's age was 1 year more than twice jill's. six years from now, his will be 10 years more than half her age. how old is joe?

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Question 834377: three years ago, joe's age was 1 year more than twice jill's. six years from now, his will be 10 years more than half her age. how old is joe?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Joe's age now
Let +b+ = Jill's age now
+a+-+3+ = Joe's age 3 yrs ago
+b+-+3+ = Jill's age 3 yrs ago
+a+%2B+6+ = Joe's age in 6 yrs
+b+%2B+6+ = Jill's age in 6 yrs
------------------------------
(1) +a+-+3+=+2%2A%28+b+-+3+%29+%2B+1+
(2) +a+%2B+6++=+%281%2F2%29%2A%28+b+%2B+6+%29+%2B+10+
---------------------------------
(1) +a+-+3+=+2b+-+6+%2B+1+
(1) +a+-+2b+=+-2+
(1) +-a+%2B+2b+=+2+
and
(2) +2a+%2B+12+=+b+%2B+6+%2B+20+
(2) +2a+-+b+=+14+
Multiply both sides of (1) by 2
and add (1) and (2)
(2) +2a+-+b+=+14+
(1) +-2a+%2B+4b+=+4+
+3b+=+18+
+b+=+6+
and
(1) +a+-+2b+=+-2+
(1) +a+=+2b+-+2+
(1) +a+=+12+-+2+
(1) +a+=+10+
Joe is 10 now
check:
Six yrs from now, Joe will be 16
Jill will be 12
Half her age is 6
Joe will be 1/2 of 6 + 10 = 16
OK