the easiest way to see this is to create a table.
the first table will include all students.
the second table will include only non-afternoon students (only morning and evening).
the first table that includes all students is shown below:
on campus not on campus total
morning 16.34 26.66 43
afternoon 7 21 28
evening 6.67 22.33 29
total 30.01 69.99 100
the second table includes all students who are not afternoon students.
on campus not on campus total
morning 16.34 26.66 43
evening 6.67 22.33 29
total 23.01 48.99 72
these are percent tables.
for example:
the percent of students who are morning students is 43%.
38% of these live on campus, so .38 * 43 = 16.34% of all students live on campus and are morning students.
62% of these do not live on campus, so .62 * 43 = 26.66% of all students do not live on campus and are morning students.
the second table includes only the students who are not afternoon students.
in the second table, the total of all students who are not afternoon students is equal to 72%.
in the second table, the total of all students who do not live on campus is 48.99%
this tells you that the percent of student who are not afternoon students and who do not live on campus is 48.99 / 72 = .68041666... = 68.041666...%.
this says that approximately 68.04% of the students who are not afternoon students do not live on campus.
your answer, as best i can determine, is that approximately 68.04% of the students who are not afternoon students do not live on campus.
an assumed real world example should help cement the understanding.
assume the total number of students is 25,000
43% of 25,000 = 10750
28% of 25,000 = 6250
29% of 25,000 = 7250
total of 10750 + 7250 are not afternoon students = 18000.
18000/25000 = .72 = 72% of all the students are not afternoon students.
62% of the 10750 do not live on campus = 6665.
77% of the 7250 do not live on campus = 5582.5
total of the 18000 who do not live on campus is 12247.5
this is equal to 12247.5 / 18000 = roughly 68.04%
numbers check out so the solution appears to be good whether you work with percents or assumed actual numbers.