SOLUTION: Carole's age 8 years ago was 5 times Carl's age. Five years ago Carole's age was 3 times Carl's age. How old is each now?

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Carole's age 8 years ago was 5 times Carl's age. Five years ago Carole's age was 3 times Carl's age. How old is each now?       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1089889: Carole's age 8 years ago was 5 times Carl's age. Five years ago Carole's age was 3 times Carl's age. How old is each now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Carole's age now
Let +b+ = Carl's age now
-----------------------------
(1) +a+-+8+=+5%2A%28+b+-+8+%29+
(2) +a+-+5+=+3%2A%28+b+-+5+%29+
-----------------------------
(1) +a+-+8+=+5b+-+40+
(1) +-a+%2B+5b+=+32+
and
(2) +a+-+5+=+3b+-+15+
(2) +-a+%2B+3b+=+10+
-----------------------
Subtract (2) from (1)
(1) +-a+%2B+5b+=+32+
(2) +a+-+3b+=+-10+
-----------------------
+2b+=+22+
+b+=+11+
and
(1) +-a+%2B+5b+=+32+
(1) +-a+%2B+5%2A11+=+32+
(1) +a+=+55+-+32+
(1) +a+=+23+
------------------
Carole is 23
Carl is 11
------------------
check:
(2) +a+-+5+=+3%2A%28+b+-+5+%29+
(2) +23+-+5+=+3%2A%28+11+-+5+%29+
(2) +18+=+3%2A6+
(2) +18+=+18+
OK