SOLUTION: In five years, the boy is 1/2 times as old as his uncle. Six ago the boys 1/3 times as old his uncle. What is the age of the boy now?

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Question 1093656: In five years, the boy is 1/2 times as old as his uncle. Six ago the boys 1/3 times as old his uncle. What is the age of the boy now?
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the boy's age now
Let +b+ = the uncle's age now
(1) +a+%2B+5+=+%281%2F2%29%2A%28+b+%2B+5+%29+
(2) +a+-+6+=+%281%2F3%29%2A%28+b+-+6+%29+
------------------------------
(1) +2%2A%28+a+%2B+5+%29+=+b+%2B+5+
(1) +2a+%2B+10+=+b+%2B+5+
(1) +-2a+%2B+b+=+5+
and
(2) +3%2A%28+a+-+6+%29+=+b+-+6+
(2) +3a+-+18+=+b+-+6+
(2) +3a+-+b+=+12+
---------------------------
Add (1) and (2)
(1) +-2a+%2B+b+=+5+
(2) +3a+-+b+=+12+
---------------------
+a+=+17+
and
(1) +-2a+%2B+b+=+5+
(1) +-34+%2B+b+=+5+
(1) +b+=+39+
-----------------------
The boy is 17 now
-----------------------
check:
(1) +a+%2B+5+=+%281%2F2%29%2A%28+b+%2B+5+%29+
(1) +17+%2B+5+=+%281%2F2%29%2A%28+39+%2B+5+%29+
(1) +22+=+%281%2F2%29%2A44+
(1) +22+=+22+
OK
You can check (2)

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
b, age of boy now
u, age of uncle now

The description formed into equations:
system%28b%2B5=%28u%2B5%29%2F2%2Cb-6=%28u-6%29%2F3%29

After one or two steps:
system%282b-u=-5%2C3b-u=12%29


highlight%28highlight%28b=17%29%29-----The boy now
-
highlight%28u=39%29