Question

At the north campus of a performing arts​ school, 30​% of the students are music majors. At the south​ campus, 70​% of the students are music majors. The campuses are merged into one east campus. If 46​% of the 1000 students at the east campus are music​ majors, how many students did the north and south campuses have before the​ merger?

Answer 1

The north campus had 600 students (180 music majors)

The south campus had 400 students (280 music majors)

Explanation:

x = number of students at the north campus before the merger

If the total of students for the two school is given as 1000, so:

(1000 - x) = number of students at the south campus before the merger.

The equation for music major is:

0,3x + 0,7(1000-x) = 0,46(1000)

0,3x + 700 - 0,7x = 460

0,3x - 0,7x = 460 - 700

- 0,4x = -240

x = -240/-0,4

x = 600 -----> total number of students at the north campus

600*(0,3) = 180 music majors at the north

100 - 600 = 400 ------> total number of students at the south campus

400*(0,7) = 280------>music majors at the south