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 $\square$ students. The south campus had $\square$ students.

Solution

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.

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