document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183070>Question 1183070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John went to his favorite Young Men clothing store and bought himself a new shirt, pants and pair of shoes. His pants cost twice as much as his shirt. His shoes cost $50 less than twice the cost of his pants. With 8% sales tax, he paid a total of $324. What was the cost of each of the item?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813220 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "s = cost of shirt<BR>\n" );
document.write( "p = cost of pants<BR>\n" );
document.write( "h = cost of shoes<BR>\n" );
document.write( "All costs are in dollars. These costs are before tax and they don't involve anything like coupons, discounts, sales promotions, etc.\r<BR>\n" );
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document.write( "\"his pants cost twice as much as his shirt\" means<BR>\n" );
document.write( "p = 2s\r<BR>\n" );
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document.write( "His shoes cost $50 less than twice the cost of his pants tells us that<BR>\n" );
document.write( "h = 2p-50\r<BR>\n" );
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document.write( "Plug in the previous equation we set up to get<BR>\n" );
document.write( "h = 2p-50<BR>\n" );
document.write( "h = 2(2s)-50<BR>\n" );
document.write( "h = 4s-50<BR>\n" );
document.write( "This way, we have both p and h in terms of s.\r<BR>\n" );
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document.write( "The total cost of everything, before tax, is:<BR>\n" );
document.write( "T = s+p+h<BR>\n" );
document.write( "T = s+2s+4s-50<BR>\n" );
document.write( "T = 7s-50<BR>\n" );
document.write( "Again, this is before tax.\r<BR>\n" );
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document.write( "With the 8% tax considered, we multiply that value of T by 1.08<BR>\n" );
document.write( "So 1.08*(7s-50) represents the final cost after tax is considered.\r<BR>\n" );
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document.write( "Set this equal to 324 and solve for s<BR>\n" );
document.write( "1.08*(7s-50) = 324<BR>\n" );
document.write( "7s-50 = 324/1.08<BR>\n" );
document.write( "7s-50 = 300<BR>\n" );
document.write( "7s = 300+50<BR>\n" );
document.write( "7s = 350<BR>\n" );
document.write( "s = 350/7<BR>\n" );
document.write( "s = 50<BR>\n" );
document.write( "The shirt costs $50\r<BR>\n" );
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document.write( "Use this to find the value of p<BR>\n" );
document.write( "p = 2s<BR>\n" );
document.write( "p = 2*50<BR>\n" );
document.write( "p = 100<BR>\n" );
document.write( "The pair of pants cost $100\r<BR>\n" );
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document.write( "Then use that value of p to find h<BR>\n" );
document.write( "h = 2p-50<BR>\n" );
document.write( "h = 2*100-50<BR>\n" );
document.write( "h = 200-50<BR>\n" );
document.write( "h = 150<BR>\n" );
document.write( "The pair of shoes cost $150\r<BR>\n" );
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document.write( "Or you could compute it like this<BR>\n" );
document.write( "h = 4s-50<BR>\n" );
document.write( "h = 4*50-50<BR>\n" );
document.write( "h = 200-50<BR>\n" );
document.write( "h = 150<BR>\n" );
document.write( "Either way, we get the same value of h.\r<BR>\n" );
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document.write( "Note that the total cost before sales tax is<BR>\n" );
document.write( "s+p+h = 50+100+150 = 300<BR>\n" );
document.write( "Then we pay 0.08*300 = 24 dollars in sales tax to get a total cost of 300+24 = $324<BR>\n" );
document.write( "Or we could say as a shortcut: 1.08*300 = 324<BR>\n" );
document.write( "This helps confirm the answers.\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "Shirt costs $50<BR>\n" );
document.write( "Pants cost $100<BR>\n" );
document.write( "Shoes cost $150<BR>\n" );
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