document.write( "Question 962125: At the north campus, 5% of the students in the department are men. At the south campus, 80% of the students in the department are men. After the merger, 50% of the 150 students are men. How many students were in the department at the north and south campuses before the merger? \n" ); document.write( "

Algebra.Com's Answer #587788 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = number of men on N.C.
\n" ); document.write( "Let $\"+b+\"$ = number of men on S.C.
\n" ); document.write( "--------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+150+\"$
\n" ); document.write( "(2) $\"+.05a+%2B+.8b+=+.5%2A150+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( "(2) $\"+.05a+%2B+.8b+=+75+\"$
\n" ); document.write( "(2) $\"+5a+%2B+80b+=+7500+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+5+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+5a+%2B+80b+=+7500+\"$
\n" ); document.write( "(1) $\"+-5a+-+5b+=+-750+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( " $\"+75b+=+6750+\"$
\n" ); document.write( " $\"+b+=+90+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+b+=+150+\"$
\n" ); document.write( "(1) $\"+a+=+150+-+90+\"$
\n" ); document.write( "(1) $\"+a+=+60+\"$
\n" ); document.write( "----------------
\n" ); document.write( "There were 60 men on N.C.
\n" ); document.write( "There were 90 men on S.C.
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+.05a+%2B+.8b+=+75+\"$
\n" ); document.write( "(2) $\"+.05%2A60+%2B+.8%2A90+=+75+\"$
\n" ); document.write( "(2) $\"+3+%2B+72+=+75+\"$
\n" ); document.write( "(2) $\"+75+=+75+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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