document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=458230>Question 458230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The word problem is....A retailer spent $48 to purchase a number of special mugs. Two of them were broken in the store but by sellimg each of the remaining mugs at $3 above the original cost per mug she made a total profit of $22. Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased.\r<BR>\n" );
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document.write( "If the price for n mugs is $48, how can we express the cost per mug? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #314347 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=314347\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A retailer spent $48 to purchase a number of special mugs.<BR>\n" );
document.write( " Two of them were broken in the store but by selling each of the remaining mugs<BR>\n" );
document.write( " at $3 above the original cost per mug she made a total profit of $22.<BR>\n" );
document.write( "Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased.<BR>\n" );
document.write( "If the price for n mugs is $48, how can we express the cost per mug?<BR>\n" );
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document.write( "Price paid for each mug = <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" );
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document.write( "No. of mugs sold = (n-2)<BR>\n" );
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document.write( "Selling price = <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<BR>\n" );
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document.write( "Revenue should = cost + profit<BR>\n" );
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document.write( "Total revenue = 48 + 22 = $70:<BR>\n" );
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document.write( "#sold * Price sold = total revenue<BR>\n" );
document.write( "(n-2) * [<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] = 70<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "48 + 3n - 96/n - 6 = 70<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "3n - 96/n + 48 - 6 - 70 = 0<BR>\n" );
document.write( "3n - 96/n - 28 = 0<BR>\n" );
document.write( "Multiply equation by n, forming a quadratic equation:<BR>\n" );
document.write( "3n^2 - 28n - 96 = 0<BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "(3n +8)(n-12) = 0<BR>\n" );
document.write( "Positive solution<BR>\n" );
document.write( "n = 12 mugs originally bought<BR>\n" );
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document.write( "Check<BR>\n" );
document.write( "Cost: 48/12 = $4<BR>\n" );
document.write( "Sold: 10 * 7 = $70 (cost + profit)<BR>\n" );
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document.write( " </SPAN>\n" );
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