Question 578092: At the north campus of a performing arts school,10% 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 42% 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
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! At the north campus of a performing arts school,10% 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 42% 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
:
Let n = total number in the north campus
then
.1n = music majors there
:
Let s = total number in the south campus
then
.9s = music majors there
:
We know:
n + s = 1000
and
.1n + .9s = .42(1000)
.1n + .9s = 420
Multiply by 10, subtract the 1st equation
1n + 9s = 4200
1n + 1s = 1000
---------------subtraction eliminates n, finds s
8s = 3200
s = 3200/8
s = 400 student were at the south campus (before the merger)
and
1000-400 = 600 were at the north campus
:
;
See if that works out, using the number of music majors.
.1(600) + .9(400) = 420
60 + 360 = 420
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