SOLUTION: Olan is 3 years older than Mary. One third of Olan's age is two years less then one-half his sister's age, one year ago. Find their ages now. Please help me answer this. Thank you

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Olan is 3 years older than Mary. One third of Olan's age is two years less then one-half his sister's age, one year ago. Find their ages now. Please help me answer this. Thank you      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1096774: Olan is 3 years older than Mary. One third of Olan's age is two years less then one-half his sister's age, one year ago. Find their ages now.
Please help me answer this. Thank you so much!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have to read it pretty carefully.
I'm assuming that Mary is Olan's sister.
Let +a+ = Olan's age now
Let +b+ = Mary's age now
-----------------------------
(1) +a+=+b+%2B+3+
(2) +%281%2F3%29%2Aa+=+%281%2F2%29%2A%28+b+-+1+%29+-+2+
----------------------------------
Note that +b+-+1+ is Mary's age 1 year ago
(2) +%281%2F3%29%2Aa+=+%281%2F2%29%2Ab+-+1%2F2+-+4%2F2+
(2) +%281%2F3%29%2Aa+=+%281%2F2%29%2Ab+-+5%2F2+
Multiply both sides by +6+
(2) +2a+=+3b+-+15+
(2) +-2a+%2B+3b+=+15+
-----------------------
(1) +a+-+b+=+3+
Multiply both sides of (1) by +2+
and add the equations
(1) +2a+-+2b+=+6+
(2) +-2a+%2B+3b+=+15+
------------------------
+b+=+21+
and
(1) +a+=+b+%2B+3+
(1) +a+=+21+%2B+3+
(1) +a+=+24+
-----------------------
Olan is 24
Mary is 21
--------------
check:
(2) +%281%2F3%29%2Aa+=+%281%2F2%29%2A%28+b+-+1+%29+-+2+
(2) +%281%2F3%29%2A24+=+%281%2F2%29%2A%28+21+-+1+%29+-+2+
(2) +8+=+%281%2F2%29%2A20+-+2+
(2) +8+=+10+-+2+
(2) +8+=+8+
OK