Looking for a formula is not always the way to solve problems like these. But think through the problem in common sense terms that are easy to grasp. So, what have we got? If the number of students in X is x, and the number of students in Y is y, then 69x/100 is the number of students from program X enrolling and 46.2y/100 is the number enrolling from program Y. We also have to assume that no students are in both programs. So we can easily compare numbers of students. How many more students from X will attend college than from Y? (69x - 46.2y)/100 students. What percentage is this of the number of students in X? It's (69x - 46.2y)/100 divided by 69x/100 multiplied by 100. What %ge is it of the total number of students? It's (69x - 46.2y)/100 divided by x+y multiplied by 100. If we assume that X and Y have the same number of students, then x = y and the answers are 33.04% approx. and 11.4%. Take an example. Out of 1,000 students, 500 participate in program X and a different 500 participate in Y. 69% of 500 is 345, and 46.2% is 231. The difference is 114 and this is 11.4% of the total number of students. Hope this helps.