document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144273>Question 1144273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Research shows that 14% of 6th graders in K-6 schools have tried cigarettes and 61% of 7th graders in 8-9 or 7-9 middle schools have tried cigarettes. what is the absolute increase to the nearest percent? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765359 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=765359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the increase would be calculated as follows:<BR>\n" );
document.write( "(61% - 14%) / 14% = 47% / 14% = 3.357142857 * 100 = 335.7142857% increase.\r<BR>\n" );
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document.write( "let x equal the number of kindergarten through 6th graders.<BR>\n" );
document.write( "let y equal the number of 7th to 9th graders.,\r<BR>\n" );
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document.write( "the number of kindergarten through 6th graders who have tried cigarettes would be .14 * x.\r<BR>\n" );
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document.write( "if there were no increase, the number of 7th to 9th graders who tried cigarettes would be .14 * y.\r<BR>\n" );
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document.write( "however, the number of 7th to 9th graders who tried cigarettes was .61 * y.\r<BR>\n" );
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document.write( "the increase is therefore (.61 * y - .14 * y) / (.14 * y) = .47 * y / .14 * y = .47 / .14 = 3.357142857 * 100 = 335.7142857%.\r<BR>\n" );
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document.write( "bear in mind that the number of 7th to 9th graders is not the same number as the number of kindergarten to 6th graders.\r<BR>\n" );
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document.write( "the percentages are applied to different base numbers.\r<BR>\n" );
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document.write( "that's why you need to set the base case for percentage of 7th to 9th graders.\r<BR>\n" );
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document.write( "the base case is the number of 7th to 9th graders who tried cigarettes if there were no increase in the percentage.\r<BR>\n" );
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document.write( "an example:\r<BR>\n" );
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document.write( "assume 100 kindergarten to 6th graders and 500 7th to 9th graders.\r<BR>\n" );
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document.write( "14% of 100 = 14 students out of 100 who tried cigarettes in the 6th grade.l\r<BR>\n" );
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document.write( "14% of 500 = 70 students out of 500 who tried cigarettes in the 7th through 9th grade.\r<BR>\n" );
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document.write( "61% of 500 = 305 students out of 500 who tried cigarettes in the 7th through 9th grade.\r<BR>\n" );
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document.write( "that's an increase of 305 - 70 = 235 out of 500 students in the 7th through 9th grade.\r<BR>\n" );
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document.write( "that's equal to 235 / 500 = .47 * 100 = 47% increase.\r<BR>\n" );
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document.write( "47% / 14% = 3.357142857 times more = 335.7142857% more.\r<BR>\n" );
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document.write( "3.357142857 * 70 = 235 more for a total of 305 out of 500 7th through 9th grade students.\r<BR>\n" );
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document.write( "if you assume the number of student in kindergarten through 6th grade is the same number of students in 7th through 9th grade, then the problem becomes a lot simpler, even though you get the same answer.\r<BR>\n" );
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document.write( "assume the number of students in kindergarten through 6th grade is 500.<BR>\n" );
document.write( "14% of 500 is 70.<BR>\n" );
document.write( "when these students advance to 7th through 9th grade, 61% have tried cigarettes.<BR>\n" );
document.write( "that would be 61% of 500 = 305.<BR>\n" );
document.write( "the increase is 305 - 70 = 235.<BR>\n" );
document.write( "235/70 = 3.357142857 more = 335.7142857% more.\r<BR>\n" );
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