document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=631079>Question 631079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Total cost price of certain number of identical articles is 4800..By selling the articles at 100 each,a profit equal to the cost price of 15 articles is made.Find the number of articles bought\r<BR>\n" );
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document.write( "My solun\r<BR>\n" );
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document.write( "Let the articles bought be x<BR>\n" );
document.write( "Then C.P of each article is 4800/x<BR>\n" );
document.write( "The Selling price of x articles  is 100x\r<BR>\n" );
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document.write( "The cost price of 15 items is 4800/15 = 320\r<BR>\n" );
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document.write( "So 100 x-4800/x = 320\r<BR>\n" );
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document.write( "100x^2 - 4800 = 320x\r<BR>\n" );
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document.write( "100x^2 - 320x - 4800 = 0;\r<BR>\n" );
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document.write( "10x^2-32x-480 = 0;\r<BR>\n" );
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document.write( "I am not able to find the solution.What is it I am doing wrong?? Please help me..Thanks in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #397508 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=397508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I agree with the beginning of your work:<BR>\n" );
document.write( "Let the articles bought be x<BR>\n" );
document.write( "Then C.P of each article is 4800/x<BR>\n" );
document.write( "The Selling price of x articles is 100x.<BR>\n" );
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document.write( "The mistake is in the next step.<BR>\n" );
document.write( "Buying x articles the merchant paid 4800/x for each one.<BR>\n" );
document.write( "That does not mean that the merchant would pay 4800/15=320 for each one of only 15 of those articles.<BR>\n" );
document.write( "It does not mean that the total cost for 15 articles is 320, either.<BR>\n" );
document.write( "You cannot say x=15 for this step, when the value of x is what you are trying to find.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Instead, you should think that the cost for 15 articles (at a cost per article of 4800/x, as you found before) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A%284800%2Fx%29=72000%2Fx ALIGN=MIDDLE  ALT=\"15%2A%284800%2Fx%29=72000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The merchant sells all the articles for a total of 100x, which is, of course, more than the 4800 cost of all the articles.<BR>\n" );
document.write( "The difference is the profit, that happens to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72000%2Fx ALIGN=MIDDLE  ALT=\"72000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28100x-4800=72000%2Fx%29 ALIGN=MIDDLE  ALT=\"highlight%28100x-4800=72000%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now let's solve, and then we can make sure that it makes sense.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100x-4800=72000%2Fx ALIGN=MIDDLE  ALT=\"100x-4800=72000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100x%5E2-4800x=72000 ALIGN=MIDDLE  ALT=\"100x%5E2-4800x=72000\"   DISABLED_style= \"max-width:90%; height:auto;\" > (multiplying both sides times x).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100x%5E2-4800x=72000 ALIGN=MIDDLE  ALT=\"100x%5E2-4800x=72000\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-48x=720 ALIGN=MIDDLE  ALT=\"x%5E2-48x=720\"   DISABLED_style= \"max-width:90%; height:auto;\" > (dividing both sides by 100).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-48x=720 ALIGN=MIDDLE  ALT=\"x%5E2-48x=720\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2-48x-720=0%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2-48x-720=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (subtracting 720 from both sides, to get a nice quadratic equation).<BR>\n" );
document.write( "We know that solving by factoring could be an option, because x should be a nice positive integer.<BR>\n" );
document.write( "We need two factors that multiplied equal -720, and add up to -48.<BR>\n" );
document.write( "The factors -60 and 12 work.<BR>\n" );
document.write( "The quadratic polynomial can be factored as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-48x-720=%28x-60%29%28x%2B12%29 ALIGN=MIDDLE  ALT=\"x%5E2-48x-720=%28x-60%29%28x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-48x-720=0 ALIGN=MIDDLE  ALT=\"x%5E2-48x-720=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-60%29%28x%2B12%29=0 ALIGN=MIDDLE  ALT=\"%28x-60%29%28x%2B12%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "with solutions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=60%29 ALIGN=MIDDLE  ALT=\"highlight%28x=60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-12 ALIGN=MIDDLE  ALT=\"x=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Of course we know that x, the number of articles bought and sold, is not a negative number, so we realize that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-12 ALIGN=MIDDLE  ALT=\"x=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be discarded because it does not make sense.<BR>\n" );
document.write( "The merchant bought <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2860%29 ALIGN=MIDDLE  ALT=\"highlight%2860%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > articles for a total of 4800 (dollars, or whatever the currency is).<BR>\n" );
document.write( " <BR>\n" );
document.write( "COMMON SENSE VERIFICATION:<BR>\n" );
document.write( "The cost per article was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4800%2F60=80 ALIGN=MIDDLE  ALT=\"4800%2F60=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "On selling the 60<BR>\n" );
document.write( "articles at 100 each, the merchant collected <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2A60=6000 ALIGN=MIDDLE  ALT=\"100%2A60=6000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The profit was the 6000 collected minus the 4800 cost, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6000-4800=1200 ALIGN=MIDDLE  ALT=\"6000-4800=1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The cost of 15 item was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A80=1200 ALIGN=MIDDLE  ALT=\"15%2A80=1200\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the same amount as the total profit.<BR>\n" );
document.write( "If the merchant had borrowed the original 4800 (from a relative, in a no-interest loan), the loan can now be repaid, and the merchant is left with 1200 to use to buy maybe 15 more of those articles (assuming he/she can still get the same good price from his supplier). </SPAN>\n" );
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