document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=361922>Question 361922</A>: <I><SPAN STYLE=\"word-break: break-all;\">  You go to a local mechanic to get your tires changed. The tires cost $300. There is a 6% sales tax, but you get a 10% discount. There is also a $10 non-taxable disposal fee for your old tires, which the mechanic tells you is not subject to discount.\r<BR>\n" );
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document.write( "Write a function, t(x) for the total purchase amount after taxes but before discounts and fees.Does it matter whether the mechanic adds the tax first or takes the discount first? <BR>\n" );
document.write( " I really need some help with this problem everything I have tried hasn't been right. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257976 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=257976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> tires cost $300.<BR>\n" );
document.write( "6% sales tax.<BR>\n" );
document.write( "10% discount.<BR>\n" );
document.write( "$10 disposal fee for old tires not subject to discount.\r<BR>\n" );
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document.write( "your formula if the discount is applied first would be as follows:\r<BR>\n" );
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document.write( "x = cost of the tires.\r<BR>\n" );
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document.write( "t(x) = (.9*x + 10) * 1.06\r<BR>\n" );
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document.write( "if x = 300, then the cost is (.9*300 + 10) * 1.06 = (270+10)*1.06 = 280*1.06 = $296.80\r<BR>\n" );
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document.write( "if the tax is applied first and then the discount is applied, your formula would be as follows:\r<BR>\n" );
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document.write( "t(x) = (x+10)*1.06 - (.1*x)\r<BR>\n" );
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document.write( "if x is equal to $300, the cost is $310*1.06 - .1*300 =  = $328.60 - $30 = $298.60.\r<BR>\n" );
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document.write( "you pay more if the tax is applied first.\r<BR>\n" );
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document.write( "your discounted price of .9*x stems from x - .10*x which becomes (1-.10)*x which becomes .9*x\r<BR>\n" );
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document.write( "your cost with tax stems from y + .06*y = (1 + .06)*y = 1.06*y.\r<BR>\n" );
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document.write( "y is the amount of the cost that is taxed.\r<BR>\n" );
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document.write( "if the discount is applied first, then y is equal to (.9*x + 10).\r<BR>\n" );
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document.write( "if the discount is applied after, then y is equal to (x+10).\r<BR>\n" );
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document.write( "so we'll go through it again, just to make sure you understand what is happening.\r<BR>\n" );
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document.write( "cost is 300.<BR>\n" );
document.write( "apply discount first and the cost is 270.<BR>\n" );
document.write( "add 10 to make the total cost 280.<BR>\n" );
document.write( "tax 6% * 280 + 280 = 296.8\r<BR>\n" );
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document.write( "tax first and the cost without the discount is 300 + 10 = 310.<BR>\n" );
document.write( "tax 6% * 310 + 310 = 328.6<BR>\n" );
document.write( "subtract discount of 30 to make a total of 298.60.\r<BR>\n" );
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document.write( "the difference in the tax you paid is the difference of the tax on the undiscounted price versus the tax on the discounted price.\r<BR>\n" );
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document.write( "the difference is 298.6 - 296.8 = 1.80\r<BR>\n" );
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document.write( ".06 * 30 = 1.8\r<BR>\n" );
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document.write( "the difference is the tax on the discount.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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