document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #370588 by ankor@dixie-net.com(22740)\"\" \"About 
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At the north campus of a performing arts school,10% of the students are music majors.
\n" ); document.write( "At the south campus,90% of the students are music majors.
\n" ); document.write( " The campuses are merged into one east campus.
\n" ); document.write( " 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
\n" ); document.write( ":
\n" ); document.write( "Let n = total number in the north campus
\n" ); document.write( "then
\n" ); document.write( ".1n = music majors there
\n" ); document.write( ":
\n" ); document.write( "Let s = total number in the south campus
\n" ); document.write( "then
\n" ); document.write( ".9s = music majors there
\n" ); document.write( ":
\n" ); document.write( "We know:
\n" ); document.write( "n + s = 1000
\n" ); document.write( "and
\n" ); document.write( ".1n + .9s = .42(1000)
\n" ); document.write( ".1n + .9s = 420
\n" ); document.write( "Multiply by 10, subtract the 1st equation
\n" ); document.write( "1n + 9s = 4200
\n" ); document.write( "1n + 1s = 1000
\n" ); document.write( "---------------subtraction eliminates n, finds s
\n" ); document.write( "8s = 3200
\n" ); document.write( "s = 3200/8
\n" ); document.write( "s = 400 student were at the south campus (before the merger)
\n" ); document.write( "and
\n" ); document.write( "1000-400 = 600 were at the north campus
\n" ); document.write( ":
\n" ); document.write( ";
\n" ); document.write( "See if that works out, using the number of music majors.
\n" ); document.write( ".1(600) + .9(400) = 420
\n" ); document.write( "60 + 360 = 420 \n" ); document.write( "
\n" );