SOLUTION: If the average of a and 2b is 26, the average of b and 2c is 41, and the average of c and 2a is 23, what is the average of a,b,and c?

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Question 1040772: If the average of a and 2b is 26, the average of b and 2c is 41, and the average of c and 2a is 23, what is the average of a,b,and c?
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%2B2b%29%2F2=26
a%2B2b=52
.
.
%28b%2B2c%29%2F2=41
b%2B2c=82
.
.
%28c%2B2a%29%2F2=23
c%2B2a=46
Adding them all together,
a%2B2b%2Bb%2B2c%2Bc%2B2a=52%2B82%2B46
3a%2B3b%2B3c=180
a%2Bb%2Bc=60
So then,
%28a%2Bb%2Bc%29%2F3=60%2F3
%28a%2Bb%2Bc%29%2F3=highlight%2820%29

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
If the average of a and 2b is 26, the average of b and 2c is 41, and the average of c and 2a is 23, what is the average of a,b,and c?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

You are given that

a + 2b = 2*26 = 52,   (1)
b + 2c = 2*41 = 82,   (2)   and
c + 2a = 2*23 = 46.   (3)

Add all three equations (both left and right sides). You will get 

3a + 3b + 3c = 52 + 82 + 46 = 180.

Divide both sides by 3. You will get

a + b + c = 180%2F3 = 60.

Answer.  The average of a, b and c is %28a%2Bb%2Bc%29%2F3%29 = 60%2F3 = 20.