In AIT, all hecturers are either in a full time faculty or a part time faculty. There are more
than twice as many lecturers in full time faculty as in part time faculty. The arithmetic mean
salary is $25,000 for the full time faculty and $35,000 for the part time faculty. What do you think could be the average salary for all of the faculty? what if there were exactly twice as many lecturers in full time faculty as in part time faculty?

$3166.67 for exactly twice as many, more  if it is more than twice as many.  

Step-by-step explanation:

The average will always be between between the two numbers, and since there are more full time lecturers the average will be closer to that value, so the higher value.  This is especially true if there are twice as many or more.  The more there are as a difference between the two the closer it will be to the one that has more.

Let's say there are x part time and y full time.  the average works out to be (x*25,000 + y*35000)/(x+y).  Now, if there are exactly twice as many full time instead of part time then you can put y = 2x and you can solve for a number.

(x*25,000 + y*35000)/(x+y)

(x*25,000 + 2x*35000)/(x+2x)

95,000x/3x

3166.67

So indeed, this is closer to 35000 than 25000, and also is the minimum for the first part since this only gets higher if there are more than twice as many full time than part time.  

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

whats the