SOLUTION: olan is 3 years older than his sister rose. 1/2 of olan's age is 13 years more than 1/4 his sister's age one year ago. find their ages now.

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Question 566003: olan is 3 years older than his sister rose. 1/2 of olan's age is 13 years more than 1/4 his sister's age one year ago. find their ages now.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Olan's age now
Let +b+ = Rose's age now
given:
(1) +a+=+b+%2B+3+
(2) +%281%2F2%29%2Aa+=+%281%2F4%29%2A%28+b+-+1+%29+%2B+13+
-----------------------------
Multiply both sides of (2) by +4+
(2) +2a+=+b+-+1+%2B+52+
(2) +2a+-+b+=+51+
Substitute (1) into (2)
(2) +2%2A%28+b+%2B+3+%29+-+b+=+51+
(2) +2b+%2B+6+-+b+=+51+
(2) +b+=+51+-6+
(2) +b+=+45+
and
(1) +a+=+b+%2B+3+
(1) +a+=+45+%2B+3+
(1) +a+=+48+
Olan's age is 48 now
Rose's age 45 now
check:
(2) +%281%2F2%29%2Aa+=+%281%2F4%29%2A%28+b+-+1+%29+%2B+13+
(2) +%281%2F2%29%2A48+=+%281%2F4%29%2A%28+45+-+1+%29+%2B+13+
(2) +24+=+44%2F4+%2B+13+
(2) +24+=+24+
OK