Question 1166699
.


In my post, I will response part (a) only.


<pre>
Enrollment at college A   {{{E[A]}}} = 12500 + 800*(n-2011).


Enrollment at college B   {{{E[B]}}} = 24200 - 500*(n-2011).


We want to know when it will happen  {{{E[A]}}} = {{{E[B]}}}.


We write the equation


    12500 + 800*(n-2011) = 24200 - 500*(n-2011)


We simplify it


    800*(n-2011) + 500*(n-2011) = 24200 - 12500

    (800+500)*(n-2011) = 11700

     1300*(n-2011) = 11700

          n - 2011 = 1170/1300 = 9.


The long-waited event will happen at the year  9 + 2011 = 2020.                                     <U>ANSWER</U>


The number of enrolled students will be  12500 + 800*9 = 19700 = 24200 - 500*9  in each college.    <U>ANSWER</U>
</pre>

Solved.


--------------


What is written next in your post - is a riddle to me . . .