SOLUTION: If the average of 27-x, x-8, and 3x+11 is y, what is the average of 2y and {{{2y/3}}} in terms of x?

Algebra ->  Average -> SOLUTION: If the average of 27-x, x-8, and 3x+11 is y, what is the average of 2y and {{{2y/3}}} in terms of x?      Log On


   

Question 972224: If the average of 27-x, x-8, and 3x+11 is y, what is the average of 2y and 2y%2F3 in terms of x?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
If the average of 27-x, x-8, and 3x+11 is y, what is the average of 2y and 2y%2F3 in terms of x?
...the average of 27-x, x-8, and 3x+11 is y...
To average them, we add them and divide by 3, then set equal to y:

%28%2827-x%29%2B%28x-8%29%2B%283x%2B11%29%29%2F3%22%22=%22%22y

Simplify

%2827-x%2Bx-8%2B3x%2B11%29%2F3%22%22=%22%22y

%2830%2B3x%29%2F3%22%22=%22%22y

%283%2810%2Bx%29%29%2F3%22%22=%22%22y

%28cross%283%29%2810%2Bx%29%29%2Fcross%283%29%22%22=%22%22y

10%2Bx%22%22=%22%22y

...what is the average of 2y and 2y%2F3 in terms of x?...
First we average 2y and 2y%2F3, then we'll substitute 10+x
for y:

To average them, we add them and divide by 2:

%282y%2B2y%2F3%29%2F2

Simplify by Multiplying top and bottom by 3:

%283%282y%29%2B3%282y%2F3%29%29%2F%283%2A2%29

%286y%2B2y%29%2F6

%288y%29%2F6

%284y%29%2F3

Now we substitute 10+x for y

%284%2810%2Bx%29%29%2F3

Edwin