SOLUTION: Patrick is four years younger than his sister Alice. In 5 years, Patrick will be 3/4 as old as Alice. How old is Patrick now?

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Question 777621: Patrick is four years younger than his sister Alice. In 5 years, Patrick will be 3/4 as old as Alice. How old is Patrick now?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = Patrick's age now
Let +a+ = Alice's age now
------------------------
(1) +p+=+a+-+4+
(2) +p+%2B+5+=+%283%2F4%29%2A%28+a+%2B+5+%29+
--------------------------
(2) +4%2A%28+p+%2B+5+%29+=+3%2A%28+a+%2B+5+%29+
(2) +4p+%2B+20+=+3a+%2B+15+
(2) +3a+-+4p+=+5+
and
(1) +p+=+a+-+4+
(1) +a+-+p+=+4+
---------------
Multiply both sides of (1) by +3+
and subtract (2) from (1)
(1) +3a+-+3p+=+12+
(2) +-3a+%2B+4p+=+-5+
+p+=+7+
and
(1) +a+-+p+=+4+
(1) +a+-+7+=+4+
(1) +a+=+11+
Patrick is 7 now
check:
(2) +p+%2B+5+=+%283%2F4%29%2A%28+a+%2B+5+%29+
(2) +7+%2B+5+=+%283%2F4%29%2A%28+11+%2B+5+%29+
(2) +12+=+%283%2F4%29%2A16+
(2) +4%2A12+=+3%2A16+
(2) +48+=+48+
OK