SOLUTION: At the north campus of a small liberal arts college, 10% of the students are women. At the south campus, 50% of the students are women. The campuses are merged into one east camp
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Question 356190: At the north campus of a small liberal arts college, 10% of the students are women. At the south campus, 50% of the students are women. The campuses are merged into one east campus. If 40% of the 1200 students at the east campus are women, how many students did each of the north and south campuses have before the merger? Answer by jrfrunner(365) (Show Source):
You can put this solution on YOUR website! At the north campus of a small liberal arts college, 10% of the students are women. At the south campus, 50% of the students are women. The campuses are merged into one east campus. If 40% of the 1200 students at the east campus are women, how many students did each of the north and south campuses have before the merger?
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let N=total students at North campus
Let S=total students at South campus
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given
North campus merged with South campus to create east campus of 1200 students
eq 1, total students: N+S=1200
eq 2, women: 0.10N+0.50S=0.40*1200=480
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step 1: N+5S=4800 multiply eq 2 by 10
step 2: N=1200-S solve for N in eq1
step 3: (1200-S)+5S=4800 substitute step 2 into step 1
step 4: 4S=3600 group similar terms
step 5: S=900
step 6: N=1200-S therefore N=1200-900=300
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validate
go to eq1 and eq2 substitute S=900 and N=300
N+S=300+900=1200 checked
0.1N+0.5S=480 ==> 0.1*300+0.5*900=30+450=480 checked
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answer ,
