42 students and 6 faculty members at byrd middle school chose to retake their school pics .these #'s represent 1/12 of the students and 1/6 of the fuculty .what is the combined # of students and faculty members

Faculty (not fuculty)    ;)

Let s = # of students and f = # of faculty.  We want to find s + f.

(1/12)s = 42.  Mult. both sides by 12, we get s = 504.

(1/6)f = 6.  Mult. both sides by 6, we get f = 36.

Then the total # of faculty and students combined is 504+36 = 540 (ans.)