Problem

At the north campus of a performing arts school, 60% of the students are music majors. At the south campus, 90% of the students are music majors. The campuses are merged into one east campus. If 69% of the 1000 students at the east campus are music majors, how many students did each of the north and south campuses have before the merger?

The north campus had students.
The south campus had students.

Answer

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Answer

The south campus had 300 students.

Steps

Step 1 :Let N be the number of students from the north campus and S be the number of students from the south campus.

Step 2 :The total number of students after the merger is 1000, so N+S=1000.

Step 3 :60% of the students from the north campus are music majors and 90% of the students from the south campus are music majors.

Step 4 :After the merger, 69% of the 1000 students are music majors, which means there are 690 music majors in total.

Step 5 :This gives us the second equation: 0.60N+0.90S=690.

Step 6 :Solve the system of equations N+S=1000 and 0.60N+0.90S=690 to find the values of N and S.

Step 7 :The solution to the system of equations is N=700 and S=300.

Step 8 :The north campus had 700 students.

Step 9 :The south campus had 300 students.

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