document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992436>Question 992436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write an equation  and solve.\r<BR>\n" );
document.write( "\n" );
document.write( "A clothing retailer marks up his merchandise at a rate of 150% so that he can regularly offer a 25% off sale. If the retail price of a sweater is $60, determine the retailer's cost and the sale price. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612087 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=612087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r = retail price<BR>\n" );
document.write( "c = cost<BR>\n" );
document.write( "s = sale price<BR>\n" );
document.write( "m = markup rate = 150% / 100 = 1.5<BR>\n" );
document.write( "d = discount rate = 25% / 100 = .25\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the retail price is equal to the cost plus the markup rate * the cost.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r = c + m * c<BR>\n" );
document.write( "since m = 1.5, then:<BR>\n" );
document.write( "r = c + 1.5 * c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sale price is equal to the retail price minus the discount rate * the retail price.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "s = r - d * r<BR>\n" );
document.write( "since d = .25, then:<BR>\n" );
document.write( "s = r - .25 * r\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the two equations are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r = c + 1.5 * c<BR>\n" );
document.write( "s = r - .25 * r\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given that r is equal to 60.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equations become:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "60 = c + 1.5 * c<BR>\n" );
document.write( "s = 60 - .25 * 60\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the second equation can be solved as is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "s = 60 - .25 * 60 which becomes:<BR>\n" );
document.write( "s = 60 - 15 which becomes:<BR>\n" );
document.write( "s = 45.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sale price of the sweater is 45 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the first equation requires a little manipulation, but can also be solved as is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the first equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "60 = c + 1.5 * c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms on the right side of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "60 = 2.5 * c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of the equation by 2.5 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "60 / 2.5 = c\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for c to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c = 24 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the cost of the sweater is 24 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you now have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the cost of the sweater is 24 dollars.<BR>\n" );
document.write( "the sale price of the sweater is 45 dollars.<BR>\n" );
document.write( "the retail price of the sweater is 60 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "below is a little extra information.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the gross profit is equal to the sale price minus the cost which is equal to 45 minus 24 = 21 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the gross profit margin is equal to the gross profit divided by the cost which is equal to 21 / 24 = .875 * 100 = 87.5%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );