Professor Ratner taught a large calculus class of 124 students. To determine if SAT mathematics scores predicted success in calculus, he kept records by three groups of SAT scores: Group I, over 600; Group II, 500–600; and Group III, below 500. After the first exam, 14 students dropped the course: 5% of Group I, 12.5% of Group II, and 25% of Group III. After the second exam, more students dropped the course. The number of students remaining was 99: being 90% of the original Group I, 82.5% of the original Group II, and 50% of the original Group III. Find the number in each group at the beginning of the course.
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