SOLUTION: THere was a young boy and girl who worked in the market. When the boy was born, the young girl was a quarter of the age of the butcher, Tony. The young girl is currently a third of

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Question 849149: THere was a young boy and girl who worked in the market. When the boy was born, the young girl was a quarter of the age of the butcher, Tony. The young girl is currently a third of the age of Gary, who is a chicken farmer. The young boy is a quarter of Tony's age. In four years he will be a quarter of Gary's age at that time. How old is the boy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Wow! Wasn't that the cast of "Green Acres" ?
Let +b+ = the Boy's age now
Let +y+ = the young girl's age now
Let +t+ = Tony's age now
Let +g+ = Gary's age now
------------------------------
(1) +y+=+%281%2F3%29%2Ag+
(2) +b+=+%281%2F4%29%2At+
(3) +b+%2B+4+=+%281%2F4%29%2A%28+g%2B4+%29+
------------------------------
When the boy was born, the young girl was
a quarter of the age of the butcher, Tony.
That means the difference in their ages,
(4) +y+-+b+=+%281%2F4%29%2At+
---------------
(2) +t+=+4b+
Substitute (2) into (4)
(4) +y+-+b+=+%281%2F4%29%2A4b+
(4) +4y+-+4b+=+4b+
(4) +y+-+b+=+b+
(4) +y+=+2b+
------------------
(1) +g+=+3y+
Substitute (1) into (3)
(3) +b+%2B+4+=+%281%2F4%29%2A%28+3y%2B4+%29+
(3) +4b+%2B+16+=+3y+%2B+4+
(3) +3y+=+4b+%2B+12+
and, from (4),
(4) +3y+=+6b+
By substitution:
+6b+=+4b+%2B+12+
+2b+=+12+
+b+=+6+
----------------
(4) +y+=+2b+
(4) +y+=+12+
and
(2) +t+=+4b+
(2) +t+=+4%2A6+
(2) +t+=+24+
----------------
(1) +g+=+3y+
(1) +g+=+3%2A12+
(1) +g+=+36+
----------------
The boy is 6
check:
(4) +y+-+b+=+%281%2F4%29%2At+
(4) +12+-+6+=+%281%2F4%29%2A24+
(4) +6+=+6+
and
(3) +b+%2B+4+=+%281%2F4%29%2A%28+g%2B4+%29+
(3) +6+%2B+4+=+%281%2F4%29%2A%28+36%2B4+%29+
(3) +10+=+%281%2F4%29%2A40+
(3) +10+=+10+
OK