document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123865>Question 1123865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Amelia is at looking at a sweater that costs $80. The store is having a 20% off sale and there is 8% sales tax Amelia is wondering which would cost less to take the 20% off then add the 8% tax or to add on the 8% sales tax then to take the 20% off. Help Amelia figure out which would cost less. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740240 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=740240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sweater is on sale for $80.00\r<BR>\n" );
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document.write( "take the discount first and then pay the sales tax equals .8 * $80 * 1.07\r<BR>\n" );
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document.write( "pay the sales tax first and then take the discount equals $80 * 1.07 * .8\r<BR>\n" );
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document.write( "i think it will wind up being the same.\r<BR>\n" );
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document.write( "breaking it down into more detail.\r<BR>\n" );
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document.write( "the price is $80.00<BR>\n" );
document.write( "20% off is .2 * $80.00 = $16.00<BR>\n" );
document.write( "$80.00 - $16.00 = $64 sale price<BR>\n" );
document.write( "7% sales tax on $64 = $4.48.<BR>\n" );
document.write( "$64 + $4.48 = $68.48 total\r<BR>\n" );
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document.write( "the price is $80.00<BR>\n" );
document.write( "7% sales tax on $80 = $5.60<BR>\n" );
document.write( "$80.00 + $5.60 = $85.60<BR>\n" );
document.write( "20% off is .2 * $85.60 = $17.12<BR>\n" );
document.write( "$85.60 - $17.12 = $68.48 total\r<BR>\n" );
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document.write( "the total price is the same.\r<BR>\n" );
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document.write( "this has to do with the commutative law of multiplication that states that a * b is the same as b * a.\r<BR>\n" );
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document.write( "20% discount is the same as multiplying the price by .8<BR>\n" );
document.write( "7% sales tax is the same as multiplying the price by 1.07\r<BR>\n" );
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document.write( ".8 * $80 * 1.07 is the same as 1.07 * $80 * .8\r<BR>\n" );
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document.write( "the .8 factor is achieved in the following manner.\r<BR>\n" );
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document.write( "x - .2 * x = x * (1 - .2) = x * .8 = .8 * x\r<BR>\n" );
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document.write( "the 1.07 factor is achieved in the following manner.\r<BR>\n" );
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document.write( "x + .07 * x = x * (1 + .07) = x * 1.07 = 1.07 * x\r<BR>\n" );
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document.write( " </SPAN>\n" );
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