Answer
year $2027$. $32100$ students.
Work Step by Step
Step 1. Assume $x$ years will be needed. We have the number of students at college A as $N1=14100+1500x$, and the number of students at college B as $N2=41700-800x$.
Step 2. Let $N1=N2$. We have $14100+1500x=41700-800x$, which gives $2300x=27600$ and $x=12$ years, which corresponds to year $2015+12=2027$.
Step 3. At $x=12$, we have $N1=14100+1500(12)=32100$ students.
