SOLUTION: a man is twice as old as his sister,and half as old as their uncle.in 50 years,his sister will be half as old as their uncle. how old is the man now?

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Question 885519: a man is twice as old as his sister,and half as old as their uncle.in 50 years,his sister will be half as old as their uncle.
how old is the man now?


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = the man's age now
Let +s+ = his sister's age now
Let +u+ = uncles age now
given:
(1) +m+=+2s+
(2) +m+=+%281%2F2%29%2Au+
(3) +s+%2B+50+=+%281%2F2%29%2A%28+u+%2B+50+%29+
------------------------------
This is 3 equations and 3 unknowns
so it's solvable
(3) +2%2A%28+s+%2B+50+%29+=+u+%2B+50+
(3) +2s+%2B+100+=+u+%2B+50+
(3) +u+=+2s+%2B+50+
-----------------------
Substitute (3) into (2)
(2) +m+=+%281%2F2%29%2A%28+2s+%2B+50+%29+
(2) +2m+=+2s+%2B+50+
(2) +m+=+s+%2B+25+
-------------------
Substitute (1) into (2)
(2) +2s+=+s+%2B+25+
(2) +s+=+25+
----------------
(3) +u+=+2s+%2B+50+
(3) +u+=+2%2A25+%2B+50+
(3) +u+=+100+
---------------
(1) +m+=+2s+
(1) +m+=+50+
----------------
The man is 50
His sister is 25
Their uncle is 100
-----------------
check:
(3) +s+%2B+50+=+%281%2F2%29%2A%28+u+%2B+50+%29+
(3) +25+%2B+50+=+%281%2F2%29%2A%28+100+%2B+50+%29+
(3) +75+=+%281%2F2%29%2A150+
(3) +150+=+150+
OK