document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=2792>Question 2792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Students sent flowers costing $20 to a sick classmate. There were 4 fewer students contributing than was planned, requiring of the others to pay 25 cents more than their original share. How many students contributed to buying the flowers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1231 by </B><A HREF=/tutors/aboutme.mpl?userid=xcentaur><B>xcentaur(357)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=xcentaur><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the total number of students supposed to be contributing be 'x'.\r<BR>\n" );
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document.write( "Let cost of each student be M = 20/x.\r<BR>\n" );
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document.write( "Now,actual number of students contributing = (x-4).\r<BR>\n" );
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document.write( "Let actual cost of each student be N = 20/(x-4).\r<BR>\n" );
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document.write( "When there were 4 students less,they paid 25 cents more.\r<BR>\n" );
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document.write( "This means that N > M by 25 cents.\r<BR>\n" );
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document.write( "Therefore,\r<BR>\n" );
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document.write( " N-M=25 Cents or $(1/4)\r<BR>\n" );
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document.write( "Then we get,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2820%2F%28x-4%29%29+-+%2820%2Fx%29+=+%281%2F4%29+ ALIGN=MIDDLE  ALT=\"+%2820%2F%28x-4%29%29+-+%2820%2Fx%29+=+%281%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Taking the LCM we get,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2820%28x%29+-+20%28x-4%29%29%2F%28x%28x-4%29%29+=+%281%2F4%29+ ALIGN=MIDDLE  ALT=\"+%2820%28x%29+-+20%28x-4%29%29%2F%28x%28x-4%29%29+=+%281%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2820x+-+20x+%2B+80%29%2F%28x%5E2+-+4x%29+=+%281%2F4%29+ ALIGN=MIDDLE  ALT=\"+%2820x+-+20x+%2B+80%29%2F%28x%5E2+-+4x%29+=+%281%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+80%2F%28x%5E2+-+4x%29+=+%281%2F4%29+ ALIGN=MIDDLE  ALT=\"+80%2F%28x%5E2+-+4x%29+=+%281%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<br>\r<BR>\n" );
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document.write( "On cross multiplying we get,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28320%29+=+%28x%5E2+-+4x%29+ ALIGN=MIDDLE  ALT=\"+%28320%29+=+%28x%5E2+-+4x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<br>\r<BR>\n" );
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document.write( "Taking 320 to the other side we get,\r<BR>\n" );
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document.write( "x^2 - 4x - 320 = 0\r<BR>\n" );
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document.write( "Factorizing 320 to get a difference of 4 we get,\r<BR>\n" );
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document.write( "x^2 - 16x + 20x - 320 = 0<BR>\n" );
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document.write( "x(x-16) + 20(x-16) = 0<BR>\n" );
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document.write( "(x-16)(x+20) = 0<BR>\n" );
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document.write( "Then we get,<BR>\n" );
document.write( "x=16 OR x=-20<BR>\n" );
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document.write( "As number of students cannot be negative,<BR>\n" );
document.write( "x=16 is the required value of x.<BR>\n" );
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document.write( "Then number of students contributing is (x-4) = 12 students.\r<BR>\n" );
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document.write( "ANS: 12 students contributed.\r<BR>\n" );
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document.write( "Hope this helped,<BR>\n" );
document.write( "Best of luck. </SPAN>\n" );
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