Answer:
374.125 students. Not sure if you're supposed to round up or down considering you can't have a fraction of a person, but I would round down.
Step-by-step explanation:
(5/8) (584) = 365 seventh graders in total
(3/8) (584) = 219 eighth graders in total
(4/8) (365) = 182.5 seventh graders who participated in track-and-field day
(7/8) (219) = 191.625 eighth graders who participated in track-and-field day
182.5 + 191.625 = 374.125 students in total who participated