At the north campus of a performing arts school, 20% of the students are music majors. At the south campus, 70% of the students are music majors. The campuses are merged into one east campus. If 30% of the 1000 students at the east campus are music majors, how many students did the north and south campuses have before the merger?

The north campus had while the south campus had .

Step-by-step explanation:

The question stated that there are students in the merged campus. That's the sum of the number of students in the north and the south campus before the merger.

Let denote the number of students in the north campus before the merger. The other students would all belong to the south campus before the merger.

Before the merger, of the students of the north campus are of music majors. In terms of , that's students.

On the other hand, of the students of the south campus are of music majors. That corresponds to students.

With a similar logic, the number of music students in the merged east campus will be .

The question implies that the sum of students in the two campuses should be equal to the number of music students in the east campus. That is:

.

Solve for :

.

In other words, there are students in the north campus and students in the south campus before the merger.

step-by-step explanation: