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?
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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 {{{highlight_red(N=300)}}}, {{{highlight_red(S=900)}}}