document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=67920>Question 67920</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395430526/algebrahomeworkh>Algebra:Structure and Method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The $75 dollar cost for a party was to be shared equally by all those attending. Since 5 more people attended than was expected, the price per person dropped by 50 cents. How many people attended the party? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48300 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=48300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The total cost of the party is =  $ 75\r<BR>\n" );
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document.write( "Let x be the number of people that have attended the party. \r<BR>\n" );
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document.write( "Let the price divided by all the people who have attended the party is =  y \r<BR>\n" );
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document.write( "Hence, the equation will be: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2875%2Fx%29+=+y ALIGN=MIDDLE  ALT=\"%2875%2Fx%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --------------->(1) \r<BR>\n" );
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document.write( "Now it is given that 5 more people attended the party. So it is x + 5 \r<BR>\n" );
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document.write( "And the amount to be shared is reduced by 50 cents.\r<BR>\n" );
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document.write( "So it is, y - 0.50 \r<BR>\n" );
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document.write( "Hence, the equation will be: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2875%2F%28x%2B5%29%29+=+y+-+0.50 ALIGN=MIDDLE  ALT=\"%2875%2F%28x%2B5%29%29+=+y+-+0.50\"   DISABLED_style= \"max-width:90%; height:auto;\" >   ----------------->(2) \r<BR>\n" );
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document.write( "Substituting EQN (1) in EQN (2), we get: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2875%2F%28x%2B+5%29%29+=+%2875%2Fx%29+-+0.50 ALIGN=MIDDLE  ALT=\"%2875%2F%28x%2B+5%29%29+=+%2875%2Fx%29+-+0.50\"   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=+0.50+=+%2875%2Fx%29-+%2875%2F%28x%2B+5%29%29 ALIGN=MIDDLE  ALT=\"+0.50+=+%2875%2Fx%29-+%2875%2F%28x%2B+5%29%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=+0.50+=+%2875%28x+%2B+5%29+-+75x%29%2F%28x%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"+0.50+=+%2875%28x+%2B+5%29+-+75x%29%2F%28x%28x%2B5%29%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=0.50+=+%2875x+%2B+375+-+75x%29%2F%28x%28x+%2B+5%29%29 ALIGN=MIDDLE  ALT=\"0.50+=+%2875x+%2B+375+-+75x%29%2F%28x%28x+%2B+5%29%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=0.50+=+375%2Fx%28x+%2B+5%29 ALIGN=MIDDLE  ALT=\"0.50+=+375%2Fx%28x+%2B+5%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=0.50x%28x+%2B+5%29+=+375 ALIGN=MIDDLE  ALT=\"0.50x%28x+%2B+5%29+=+375\"   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=%281%2F2%29x%28x+%2B+5%29+=+375 ALIGN=MIDDLE  ALT=\"%281%2F2%29x%28x+%2B+5%29+=+375\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x(x + 5) = 375 * 2 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 5x = 750 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 5x - 750 = 0 \r<BR>\n" );
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document.write( "This is a quadratic equation, hence by the Method Of Factorization we solve for the value of x. \r<BR>\n" );
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document.write( "We observe that the factors of 750 are 25 * 30 \r<BR>\n" );
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document.write( "So, the equation becomes: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 30x - 25x - 750 = 0 \r<BR>\n" );
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document.write( "x(x + 30) - 25(x + 30) = 0 \r<BR>\n" );
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document.write( "(x - 25)(x + 30) = 0 \r<BR>\n" );
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document.write( "This implies x = 25 or x = -30 \r<BR>\n" );
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document.write( "Since 30 is neagtive we cannot take the value. Hence, we take the value 25.\r<BR>\n" );
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document.write( "Thus, the total number of people that attended tha party is = 25.\r<BR>\n" );
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document.write( "Therefore, y = 25 \r<BR>\n" );
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document.write( "So when the number of people of increased by 5 then the total number of people who attended the party is y = 30 \r<BR>\n" );
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document.write( "Hence, the cost per people whould be $ 3 when the number of peopl is 25. \r<BR>\n" );
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document.write( "So when there are 30 people, the share of money to be given to the party is $2.50\r<BR>\n" );
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document.write( "I hope the steps are clear. \r<BR>\n" );
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document.write( "If you have any more queries you can get back to me on this ID. tutyfruty9@yahoo.com\r<BR>\n" );
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document.write( "Happy Calculating!!!!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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