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
The south campus had
The south campus had
Step 1 :Let
Step 2 :The total number of students after the merger is 1000, so
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:
Step 6 :Solve the system of equations
Step 7 :The solution to the system of equations is
Step 8 :The north campus had
Step 9 :The south campus had