SOLUTION: find a:b:c, given 3a+b=2c and 3b=2c+a.

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Question 1110118: find a:b:c, given 3a+b=2c and 3b=2c+a.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Use the first equation to substitute 3a+b for 2c
in the second equation:

3b = 2c+a 
3b = 3a+b+a
3b = 4a+b
2b = 4a
 b = 2a
Divide both sides by 2b, to get a/b on the right

%28b%29%2F%282b%29+=+%282a%29%2F%282b%29
1%2F2=a%2Fb
1:2 = a:b
a:b = 1:2

Substitute 2a for b in

3a+b  = 2c
3a+2a = 2c
   5a = 2c

Divide both sides by 5c to get a/c on the left:

%285a%29%2F%285c%29+=+%282c%29%2F%285c%29

a%2Fc=2%2F5

a:c = 2:5

So now we have:

a:b = 1:2
a:c = 2:5

Since 'a' corresponds to 1 in the first equation and
to 2 in the second equation, get them so that a corresponds
to the same number in both by multiplying both parts of the 
first ratio 1:2 by 2, getting 2:4

a:b = 2:4
a:c = 2:5

Now that a corresponds to the same number, 2, in both,
we can conclude:

a:b:c = 2:4:5

Edwin