document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188523>Question 188523</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534400507/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A retailer bought a number of special mugs for $48.  She decided to keep two of the mugs for herself but then had to change the price to $ 3 a mug above the original cost per mug.  If she sells the remaining mugs for $70, how many mugs didi she buy and at what price per mug did she sell them?\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141348 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=141348\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A retailer bought a number of special mugs for $48. She decided to keep two<BR>\n" );
document.write( " of the mugs for herself, but then had to change the price to $3 a mug above<BR>\n" );
document.write( " the original cost per mug. If she sells the remaining mugs for $70, <BR>\n" );
document.write( "how many mugs did she buy and at what price per mug did she sell them?<BR>\n" );
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document.write( "Let n = number of mugs she bought<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(n-2) = number of mugs sold (she kept two)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<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;\" > = original cost per mug<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F%28%28n-2%29%29 ALIGN=MIDDLE  ALT=\"70%2F%28%28n-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = price per mug she sold<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Original cost + $3 = price per mug she sold<BR>\n" );
document.write( "<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;\" > + 3 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F%28%28n-2%29%29 ALIGN=MIDDLE  ALT=\"70%2F%28%28n-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply n(n-2) to get rid of the denominators, results:<BR>\n" );
document.write( "48(n-2) + 3n(n-2) = 70n<BR>\n" );
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document.write( "48n - 96 + 3n^2 - 6n = 70n<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "3n^2 + 48n - 6n - 70n - 96 = 0<BR>\n" );
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document.write( "3n^2 - 28n - 96 = 9<BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "(3n+8)(n-12) = 0<BR>\n" );
document.write( "The positive solution is what we want here<BR>\n" );
document.write( "n = 12 mugs bought<BR>\n" );
document.write( "then<BR>\n" );
document.write( "10 mugs sold<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F10 ALIGN=MIDDLE  ALT=\"70%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = $7 price of each mug sold<BR>\n" );
document.write( ";<BR>\n" );
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document.write( "Check solution<BR>\n" );
document.write( "70/10 = $7 price<BR>\n" );
document.write( "48/12 = $4 cost<BR>\n" );
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document.write( "Mark-up=$3<BR>\n" );
document.write( "7 </SPAN>\n" );
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