document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1080864>Question 1080864</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was $22.find the amount of the bill.<BR>\n" );
document.write( "2) A shopkeeper marks the prices of his goods at 25% higher than the original price. After that he allows a discount of 12%.what profit or loss does he get? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #694944 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=694944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was 22.\r<BR>\n" );
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document.write( "find the amount of the bill.\r<BR>\n" );
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document.write( "let x equal the amount of the bill.\r<BR>\n" );
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document.write( "a discount of 35% on the bill makes the bill equal to x - .35 * x = (1 - .35) * x = .65 * x.\r<BR>\n" );
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document.write( "the first discount of 20% on the bill makes the bill equal to x - .20 * x = .80 * x.\r<BR>\n" );
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document.write( "the second discount of 20% on the bill makes the bill equal to .80 * x - .20 * .80 * x which is equal to .80 * x - .16 * x which is equal to .64 * x.\r<BR>\n" );
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document.write( "the difference between a 35% discount on the original amount and two successive discounts of 20% on the original amount is .65 * x - .64 * x which is equal to .01 * x.\r<BR>\n" );
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document.write( "that difference is equal to 22, so you get .01 * x = 22.\r<BR>\n" );
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document.write( "solve for x to get x = 22/.01 = 2200.\r<BR>\n" );
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document.write( "the original amount was 2200.\r<BR>\n" );
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document.write( "a 35% discount on the original amount was .35 * 2200 = 770.\r<BR>\n" );
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document.write( "the discounted price was therefore 2200 - 7700 = 1430.\r<BR>\n" );
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document.write( "1430 is equal to 1430/2200 * 100 = 65% of the original cost, as we had calculated earlier.\r<BR>\n" );
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document.write( "a 20% discount on the original amount was .20 * 2200 = 440.\r<BR>\n" );
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document.write( "the first discounted price was therefore 2200 - 440 = 1760.\r<BR>\n" );
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document.write( "an additional discount of 20% on this amount was .20 * 1760 = 352.\r<BR>\n" );
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document.write( "the second discounted price was therefore 1760 - 352 = 1408.\r<BR>\n" );
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document.write( "1408 is equal to 1408 / 2200 * 100 = 64% of the original cost, as we had calculated earlier.\r<BR>\n" );
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document.write( "the difference between the 35% discounted price and the 20% on top of 20% discounted price is 1430 - 1408 = 22.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "2) A shopkeeper marks the prices of his goods at 25% higher than the original price. After that he allows a discount of 12%.\r<BR>\n" );
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document.write( "what profit or loss does he get?\r<BR>\n" );
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document.write( "let x equal the original price.\r<BR>\n" );
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document.write( "he marks it up by 25% which makes the marked price equal to x + .25 * x which is equal to 1.25 * x.\r<BR>\n" );
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document.write( "he gives a discount of 12% on this marked up price.\r<BR>\n" );
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document.write( "the discounted price is equal to 1.25 * x - .12 * 1.25 * x\r<BR>\n" );
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document.write( "simplify this to get the discounted price is equal to 1.25 * x - .15 * x.\r<BR>\n" );
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document.write( "combine like terms to get the discounted price is equal to 1.10 * x.\r<BR>\n" );
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document.write( "the original price was x.\r<BR>\n" );
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document.write( "the final discounted price off the marked up price is equal to 1.10 * x.\r<BR>\n" );
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document.write( "the difference is 1.10 * x - x which is equal to .10 * x.\r<BR>\n" );
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document.write( "thismeans the profit is equal to .10 * x which is equal to 10% of x which is equal to 10% of the original price.\r<BR>\n" );
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document.write( "to see if this makes sense, let x be any value.\r<BR>\n" );
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document.write( "i let x = 1000.\r<BR>\n" );
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document.write( "the marked up price is 1000 + .25 * 1000 = 1250.\r<BR>\n" );
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document.write( "a 12% discount on the marked price makes the discounted marked up price equal to 1250 - .12 * 1250 = 1100.\r<BR>\n" );
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document.write( "the original price was 1000.\r<BR>\n" );
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document.write( "the discounted marked up price was 1100.\r<BR>\n" );
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document.write( "the profit was 1100 - 1000 = 100 which is equal to 10% of the original price.\r<BR>\n" );
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document.write( "this confirms the solution was correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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