SOLUTION: Solve and Show your solution Two years ago, Jose was 5/2 times older than his sister Maria. Ten years from now, Jose will be 3/2 times older than Maria. How old are they now?

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Solve and Show your solution Two years ago, Jose was 5/2 times older than his sister Maria. Ten years from now, Jose will be 3/2 times older than Maria. How old are they now?      Log On

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Question 1050058: Solve and Show your solution
Two years ago, Jose was 5/2 times older than his sister Maria. Ten years from now, Jose will be 3/2 times older than Maria. How old are they now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Jose's age now
Let +b+ = Maria's age now
----------------------------
(1) +a+-+2+=+%285%2F2%29%2A%28+b+-+2+%29+
(2) +a+%2B+10+=+%283%2F2%29%2A%28+b+%2B+10+%29+
-------------------------------
(1) +2a+-+4+=+5%2A%28+b-2+%29+
(1) +2a+-+4+=+5b+-+10+
(1) +-2a+%2B+5b+=+6+
and
(2) +2a+%2B+20+=+3%2A%28+b+%2B+10+%29+
(2) +2a+%2B+20+=+3b+%2B+30+
(2) +2a+-+3b+=+10+
------------------------------
Add (1) and (2)
(1) +-2a+%2B+5b+=+6+
(2) +2a+-+3b+=+10+
----------------------
+2b+=+16+
+b+=+8+
and
(2) +2a+-+3b+=+10+
(2) +2a+-+3%2A8+=+10+
(2) +2a+=+24+%2B+10+
(2) +2a+=+34+
(2) +a+=+17+
----------------------
Jose is 17
Maria is 8
-------------
check:
(1) +a+-+2+=+%285%2F2%29%2A%28+b+-+2+%29+
(1) +17+-+2+=+%285%2F2%29%2A%28+8+-+2+%29+
(1) +15+=+%285%2F2%29%2A6+
(1) +15+=+5%2A3+
(1) +15+=+15+
OK
You can check (2)