SOLUTION: 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 e

Question 406502: 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 x = no. of students originally at the north campus
;
the total for the two school is given as 1000, therefore:
(1000-x) = no. of students originally at the south campus
:
the equation for music majors
.10x + .90(1000-x) = .42(1000)
.10x + 900 - .90x = 420
.10x - .90x = 420 - 900
-.8x = -480
x =
x = +600 students at the south campus
and
1000 - 600 = 400 students at the north campus
:
:
Check this by finding the actual number of music majors at each campus:
.1(600) + .9(400) = .42(1000)
60 + 360 = 420; confirms our solutions
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