SOLUTION: The average of alex's,bonnie's and carl's ages is 9. Four years ago carl was the same age as Alex is now. In three years, Bonnie's age will be two-thirds Ales's age. How old is eac

Algebra ->  Average -> SOLUTION: The average of alex's,bonnie's and carl's ages is 9. Four years ago carl was the same age as Alex is now. In three years, Bonnie's age will be two-thirds Ales's age. How old is eac      Log On


   

Question 900556: The average of alex's,bonnie's and carl's ages is 9. Four years ago carl was the same age as Alex is now. In three years, Bonnie's age will be two-thirds Ales's age. How old is each now? I need to now how to write this in an equation?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Alex's age now
Let +b+ = Bonnie's age now
Let +c+ = Carl's age now
--------------------------
(1) +%28+a+%2B+b+%2B+c+%29+%2F+3+=+9+
(2) +c+-+4+=+a+
(3) +b+%2B+3+=+%282%2F3%29%2A%28+a+%2B+3+%29+
----------------------------
(1) +a+%2B+b+%2B+c+=+27+
and
(3) +3%2A%28+b+%2B+3+%29+=+2%2A%28+a+%2B+3+%29+
(3) +3b+%2B+9+=+2a+%2B+6+
(3) +2a+-+3b+=+3+
-------------------
(1) +c+=+27+-+a+-+b+
Substitute this result into (2)
(2) +c+-+4+=+a+
(2) +27+-+a+-+b+-+4+=+a+
(2) +2a+%2B+b+=+23+
---------------------
Subtract (3) from (2)
(2) +2a+%2B+b+=+23+
(3) +-2a+%2B+3b+=+-3+
----------------------
+4b+=+20+
+b+=+5+
and
(3) +2a+-+3b+=+3+
(3) +2a+-+3%2A5+=+3+
(3) +2a+=+3+%2B+15+
(3) +2a+=+18+
(3) +a+=+9+
and
(2) +c+-+4+=+a+
(2) +c+-+4+=+9+
(2) +c+=+13+
-----------------
Alex is 9
Bonnie is 5
Carl is 13
-------------
check:
(1) +%28+a+%2B+b+%2B+c+%29+%2F+3+=+9+
(1) +%28+9+%2B+5+%2B+13+%29+%2F+3+=+9+
(1) +27%2F3+=+9+
(1) +27+=+27+
OK