SOLUTION: Carole's age 8 years ago was 5 times Carl's age. Five years ago, Carole's age was 3 time Carl's age. How old is each now? I have already used guess & check to find out that thei

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Question 189109: Carole's age 8 years ago was 5 times Carl's age. Five years ago, Carole's age was 3 time Carl's age. How old is each now? I have already used guess & check to find out that their ages are Carl: 11 and Carole: 23, but what I need help is showing my work and learning our to create an equation from it. Thank you.
Answer by josmiceli(6784) About Me  (Show Source):
You can put this solution on YOUR website!
Let a= Carole's age now
Let b= Carl's age now
a+-+8= Carole's age 8 years ago
b+-+8= Carl's age 8 years ago
a+-+5= Carole's age 5 years ago
b+-+5= Carl's age 5 years ago
--------------
given:
(1) a+-+8+=+5%2A%28b+-+8%29
(2) a+-+5+=+3%2A%28b+-+5%29
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(1) a+-+8+=+5%2A%28b+-+8%29
(1) a+-+8+=+5b+-+40
(1) 5b+-+a+=+32
and
(2) a+-+5+=+3%2A%28b+-+5%29
(2) a+-+5+=+3b+-+15
(2) 3b+-+a+=+10
Subtract (2) from (1)
(3) 2b+=+22
(3) b+=+11
Substitute this back in (1) or (2)
(1) 5%2A11+-+a+=+32
(1) a+=+55+-+32
(1) a+=+23
Carole is 23 and Carl is 11