Answer
There will be 285 students enrolled in the program.
Work Step by Step
Let X represent the amount of students that will be enrolled in the university after the 14% increase.
A guideline for this problem would be:
After increase enrollment = Before increase enrollment + Increase in enrollment
So, X = 250 + 14% $\times$ 250
So, X = 250 + .14 $\times$ 250
X = 250 + 35
X = 285
There will be 285 students enrolled in the program.