SOLUTION: At the north campus of a college, 10% of students are music majors. At the south campus 90% of the students are music majors. Both campuses are merged into one east campus. If 42%o

Question 503671: At the north campus of a college, 10% of students are music majors. At the south campus 90% of the students are music majors. Both campuses are merged into one east campus. If 42%of the 1000 students are music majors, how many students did each of the north and south campuses have before the merger.
I tried 42%of 1000 = 420 but can't figure how to get the number of students. Help!
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
m = percentage of music majors
s = total students in south campus
n = total students on north campus
s+n = 1000
.
so
n = 1000-s
s = 1000-n
.
.10n = number of music majors on north campus
.90s = number of students in south campus
.
420 of 1000 total students are music majors
.
.1n + .9s = 420
.
substitute for s = 1000-n
.
.1n + .9(1000-n) = 420
.
multiply by 10 to remove decimals
.
n + 9(1000-n) = 4200
n + 9000 -9n = 4200
-8n = -4800
n = 600
.
s = 1000-s
s = 400
.
Always check your work.
.
.10n = .1(600) = 60
.90s = .9(400) = 360
60+360 = 420
Correct.
.
Re-read the question to make sure you answer it.
.
Answer: the north campus had 600 students, and the south campus had 400 students.
.
Done.

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