document.write( "Question 274418: At the north campus of a performing arts school, 50% of the student are music majors. At the south campus, 60% of the students are music majors. The campuses are merged into one east campus. If 55% of the 100 student at the east campus are music majors, how many students did each of the north and south campuses have before the merger? \r
\n" ); document.write( "\n" ); document.write( "Please help by showing me the formula! Thanks a bunch! \n" ); document.write( "

Algebra.Com's Answer #200271 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"n\"$ = the number of students at N Campus before merger
\n" ); document.write( "Let $\"s\"$ = the number of students at S Campus before merger
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"n+%2B+s+=+100\"$
\n" ); document.write( " $\".5n+%2B+.6s+=+.55%2A100\"$
\n" ); document.write( " $\".5n+%2B+.6s+=+55\"$
\n" ); document.write( "(2) $\"5n+%2B+6s+=+550\"$
\n" ); document.write( "Multiply both sides of (1) by $\"5\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"5n+%2B+6s+=+550\"$
\n" ); document.write( "(1) $\"-5n+-+5s+=+-500\"$
\n" ); document.write( " $\"s+=+50\"$
\n" ); document.write( "And, from (1),
\n" ); document.write( "(1) $\"n+%2B+s+=+100\"$
\n" ); document.write( " $\"n+%2B+50+=+100\"$
\n" ); document.write( " $\"n+=+50\"$
\n" ); document.write( "The N campus had 50 students and the S campus also had 50 students
\n" ); document.write( "check answer:
\n" ); document.write( " $\".5n+%2B+.6s+=+.55%2A100\"$
\n" ); document.write( " $\".5%2A50+%2B+.6%2A50+=+55\"$
\n" ); document.write( " $\"25+%2B+30+=+55\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );