Question 972224
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?

...the average of 27-x, x-8, and 3x+11 is y...
<pre>
To average them, we add them and divide by 3, then set equal to y:

{{{((27-x)+(x-8)+(3x+11))/3}}}{{{""=""}}}{{{y}}}

Simplify

{{{(27-x+x-8+3x+11)/3}}}{{{""=""}}}{{{y}}}

{{{(30+3x)/3}}}{{{""=""}}}{{{y}}}

{{{(3(10+x))/3}}}{{{""=""}}}{{{y}}}

{{{(cross(3)(10+x))/cross(3)}}}{{{""=""}}}{{{y}}}

{{{10+x}}}{{{""=""}}}{{{y}}}
</pre>
...what is the average of 2y and {{{2y/3}}} in terms of x?...
<pre>
First we average {{{2y}}} and {{{2y/3}}}, then we'll substitute 10+x
for y:

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

{{{(2y+2y/3)/2}}}

Simplify by Multiplying top and bottom by 3:

{{{(3(2y)+3(2y/3))/(3*2)}}}

{{{(6y+2y)/6}}}

{{{(8y)/6}}}

{{{(4y)/3}}}

Now we substitute 10+x for y

{{{(4(10+x))/3}}}

Edwin</pre>