Expressing the ratio the way you have implies that the number of students is proportional to the number of home-room teachers (yes).
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One would only know for sure if another data point were made available. In most real-life school districts, there are special-subject teachers, librarians, counselors, and others that count as "teachers" but are proportional to the number of schools, rather than the number of students. The total number of "teachers" is not proportional to the total number of students.