An outbreak of gastroenteritis occurred at a boarding school with a student enrollment of 846. Fifty-seven students reported symptoms including vomiting, diarrhea, nausea, and low-grade fever between 10 p.m. on September 24 and 8 p.m. on September 25. The ill students lived in dormitories that housed 723 of the students. The table below provides information on the number of students per type of residence and the number reporting illnesses consistent with the described symptoms and onset time. What is the proportion of total cases occurring in boys?
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