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 $\square$ students.
The south campus had $\square$ students.
Answer
The south campus had \( \boxed{300} \) students.
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 \( \boxed{700} \) students.
Step 9 ：The south campus had \( \boxed{300} \) students.
