document.write( "Question 406502: 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 #286814 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
\n" ); document.write( "students did each of the north and south campuses have before the merger?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of students originally at the north campus
\n" ); document.write( ";
\n" ); document.write( "the total for the two school is given as 1000, therefore:
\n" ); document.write( "(1000-x) = no. of students originally at the south campus
\n" ); document.write( ":
\n" ); document.write( "the equation for music majors
\n" ); document.write( ".10x + .90(1000-x) = .42(1000)
\n" ); document.write( ".10x + 900 - .90x = 420
\n" ); document.write( ".10x - .90x = 420 - 900
\n" ); document.write( "-.8x = -480
\n" ); document.write( "x = $\"%28-480%29%2F%28-.8%29\"$
\n" ); document.write( "x = +600 students at the south campus
\n" ); document.write( "and
\n" ); document.write( "1000 - 600 = 400 students at the north campus
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this by finding the actual number of music majors at each campus:
\n" ); document.write( ".1(600) + .9(400) = .42(1000)
\n" ); document.write( "60 + 360 = 420; confirms our solutions \n" ); document.write( "

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