document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5300>Question 5300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A retailer spent $48 to purchase a number of mugs. Two of them were broken in the store, but by selling each of the remaining mugs for $3 above the original cost per mug, she made a total profit of $22.\r<BR>\n" );
document.write( "\n" );
document.write( "If the price for n mugs is $48, how can I express the cost per mug?\r<BR>\n" );
document.write( "\n" );
document.write( "The number of mugs that are available for sale?\r<BR>\n" );
document.write( "\n" );
document.write( "Rewrite the equation from above in the standard form of a quadratic equation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2687 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is an interesting problem.  Let's start by letting <BR>\n" );
document.write( "n= number of mugs purchased by the retailer<BR>\n" );
document.write( "n-2 = number of mugs sold (two were broken and not able to be sold!)<BR>\n" );
document.write( "C = cost per mug paid by the retailer<BR>\n" );
document.write( "C + 3 = retail selling price of the mugs (for which retailer gets a $3 profit)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To answer your other questions: <BR>\n" );
document.write( "If the price for n mugs is $48, then the cost per mug is $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Fn ALIGN=MIDDLE  ALT=\"48%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The number of mugs available for sale = n-2.\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "The equation is based upon the revenue from the sale of the mugs:<BR>\n" );
document.write( "\"Selling price per mug TIMES number of mugs sold = Revenue = Cost + Profit\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28C%2B3%29%2A%28n-2%29+=+48+%2B+22 ALIGN=MIDDLE  ALT=\"+%28C%2B3%29%2A%28n-2%29+=+48+%2B+22\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=48%2Fn ALIGN=MIDDLE  ALT=\"C=48%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute for the C in this equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2848%2Fn+%2B+3%29+%28n-2%29+=+70+ ALIGN=MIDDLE  ALT=\"+%2848%2Fn+%2B+3%29+%28n-2%29+=+70+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Find the Least Common Denominator for the binomial above:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28%2848%2B+3n%29%2Fn+%29%2A+%28n-2%29+=+70 ALIGN=MIDDLE  ALT=\"++%28%2848%2B+3n%29%2Fn+%29%2A+%28n-2%29+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28%283n%2B+48%29%2Fn+%29%2A+%28n-2%29+=+70 ALIGN=MIDDLE  ALT=\"++%28%283n%2B+48%29%2Fn+%29%2A+%28n-2%29+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28%283n%5E2+-6n+%2B+48n+-96%29%2Fn+%29+=+70 ALIGN=MIDDLE  ALT=\"++%28%283n%5E2+-6n+%2B+48n+-96%29%2Fn+%29+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply both sides by the denominator \"n\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3n%5E2+%2B+42n+-+96+=+70n+ ALIGN=MIDDLE  ALT=\"+3n%5E2+%2B+42n+-+96+=+70n+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract 70n from each side of the equation to set it equal to zero:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2+%2B+42n+-+70n+-+96+=+70n-70n ALIGN=MIDDLE  ALT=\"3n%5E2+%2B+42n+-+70n+-+96+=+70n-70n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2+-+28n+-+96=+0 ALIGN=MIDDLE  ALT=\"3n%5E2+-+28n+-+96=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now this is a GREAT place to use Ichudov's new process for solving quadratic equations, but unfortunately I haven't learned it yet.  Maybe the Maestro will step in and add his touch to this solution.  Anyway, I DO know that this equation DOES factor, since if you calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4ac ALIGN=MIDDLE  ALT=\"b%5E2+-+4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get 1936 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt+%281936%29+=+44 ALIGN=MIDDLE  ALT=\"sqrt+%281936%29+=+44\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So, solve it however you can . . .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you factor it, this comes out to \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2+-+28n+-+96=+0 ALIGN=MIDDLE  ALT=\"3n%5E2+-+28n+-+96=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283n%2B8%29%28n-12%29+=+0 ALIGN=MIDDLE  ALT=\"%283n%2B8%29%28n-12%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=+-8%2F3 ALIGN=MIDDLE  ALT=\"n=+-8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=+12 ALIGN=MIDDLE  ALT=\"n=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n cannot be a negative fraction, so <BR>\n" );
document.write( "n= 12 mugs were purchased.<BR>\n" );
document.write( "n-2 = 10 mugs were sold.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Fn=+48%2F12+=+4 ALIGN=MIDDLE  ALT=\"48%2Fn=+48%2F12+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > $4 = cost to buy each mug<BR>\n" );
document.write( "Add a $3 profit to each mug = $7 for each of the 10 mugs that were sold.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check:  <BR>\n" );
document.write( "12 mugs were purchased at $4 each for a total of $48.<BR>\n" );
document.write( "10 mugs were sold at $7 each for a total of $70.  That gives a profit of $22.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "R^2 at SCC\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );