SOLUTION: In 3 years, david will be 3 times as old as his sister Marina, a year ago, David was 7 times as old as Marina. how old are they now?

Algebra ->  Linear-equations -> SOLUTION: In 3 years, david will be 3 times as old as his sister Marina, a year ago, David was 7 times as old as Marina. how old are they now?      Log On


   

Question 1103437: In 3 years, david will be 3 times as old as his sister Marina, a year ago, David was 7 times as old as Marina. how old are they now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = David's age now
Let +b+ = Marina's age now
------------------------------
(1) +a+%2B+3+=+3%2A%28+b+%2B+3+%29+
(2) +a+-+1+=+7%2A%28+b+-+1+%29+
------------------------------
(1) +a+%2B+3+=+3b+%2B+9+
(1) +a+-+3b+=+6+
and
(2) +a+-+1+=+7b+-+7+
(2) +-a+%2B+7b+=+6+
-------------------------
Add the equations
(1) +a+-+3b+=+6+
(2) +-a+%2B+7b+=+6+
-------------------------
+4b+=+12+
+b+=+3+
and
(1) +a+-+3%2A3+=+6+
(1) +a+=+9+%2B+6+
(1) +a+=+15+
---------------------
David is 15 now
Marina is 3 now
--------------------
check:
In 3 yrs David is 18
In 3 yrs Marina is 6
+18+=+3%2A6+
OK
---------------------
1 yr ago David was 14
1 yr ago Marina was 2
+14+=+7%2A2+
OK