QuestionAt the north campus of a performing arts school, of the students are music majors. At the south campus, of the students are music majors. The campuses are merged into one east campus. If 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 600 students.
The south campus had students.
Studdy Solution
STEP 1
1. The north campus had 600 students.
2. 20% of the students at the north campus are music majors.
3. The south campus had an unknown number of students.
4. 30% of the students at the south campus are music majors.
5. The east campus has a total of 1000 students.
6. 24% of the students at the east campus are music majors.
7. We need to find the number of students at the south campus before the merger.
STEP 2
1. Calculate the number of music majors at the north campus.
2. Define a variable for the number of students at the south campus.
3. Write an equation for the total number of music majors at the east campus.
4. Solve the equation to find the number of students at the south campus.
STEP 3
Calculate the number of music majors at the north campus.
STEP 4
Define a variable for the number of students at the south campus. Let be the number of students at the south campus.
STEP 5
Write an equation for the total number of music majors at the east campus.
The total number of music majors at the east campus is 24% of 1000, which is:
The number of music majors at the south campus is .
The equation becomes:
STEP 6
Solve the equation to find the number of students at the south campus.
Subtract 120 from both sides:
Divide both sides by 0.30:
The south campus had students.
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