document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964370>Question 964370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the price of oranges increase by 13.33% you have four oranges less for a rupee. how many oranges can now be had for a rupee? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589264 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=589264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have two equations.\r<BR>\n" );
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document.write( "x*p = 1 is the first equation.\r<BR>\n" );
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document.write( "x represents the number of oranges and p represents the price per orange.\r<BR>\n" );
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document.write( "13.33% divided by 100 is equal to .1333.\r<BR>\n" );
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document.write( "1.1333 * p * (x-4) is the second equation.\r<BR>\n" );
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document.write( "the price of oranges went up 13.33% which means the new price of oranges is equal to 1.1333 * p.\r<BR>\n" );
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document.write( "the number of oranges that can be bought with 1 rupee is now x-4 rather than s.\r<BR>\n" );
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document.write( "your 2 equations are:\r<BR>\n" );
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document.write( "x*p = 1<BR>\n" );
document.write( "(x-4)*(1.1333*p) = 1\r<BR>\n" );
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document.write( "these equations need to be solved simultaneously.\r<BR>\n" );
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document.write( "simplify the second equation to get:\r<BR>\n" );
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document.write( "x*1.1333*p - 4*1.1333*p = 1\r<BR>\n" );
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document.write( "in the first equation of x*p = 1, you can solve for p to get p = 1/s.\r<BR>\n" );
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document.write( "replace p with 1/x in the second equation to get:\r<BR>\n" );
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document.write( "x*1.1333*p - 4*1.1333*p = 1 becomes x*1.1333*1/x - 4*1.1333*1/x = 1\r<BR>\n" );
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document.write( "multiply both sides of this eqution by x to get:\r<BR>\n" );
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document.write( "1.1333*x - 4*1.1333 = x\r<BR>\n" );
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document.write( "subtract x from both sides of the equation and add 4*1.1333 to both sides of the equation to get:\r<BR>\n" );
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document.write( "1.1333*x - x = 4*1.1333\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".1333 * x = 4*1.1333\r<BR>\n" );
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document.write( "divide both sides of this equation by .1333 to get:\r<BR>\n" );
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document.write( "x = 4*1.1333/.1333\r<BR>\n" );
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document.write( "solve for x to get x = 34.00750188.\r<BR>\n" );
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document.write( "round this off to 34.\r<BR>\n" );
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document.write( "x is the number of oranges.\r<BR>\n" );
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document.write( "in the equation of x*p = 1, replace x with 34 to get 34*p = 1.\r<BR>\n" );
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document.write( "solve for p to get p = 1/34.\r<BR>\n" );
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document.write( "he can buy 34 oranges at 1/34 of a rupee apiece.\r<BR>\n" );
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document.write( "if the price goes up by 13.33%, then the new price is 1/34 * 1.1333 = .0333323529 rupees.\r<BR>\n" );
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document.write( "the number of oranges goes down from 34 to 30.\r<BR>\n" );
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document.write( ".0333323529 * 30 = .9999705882 which is very close to 1, so the solution is confirmed as good.\r<BR>\n" );
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document.write( "when the price goes up 13.33%, he can get 30 oranges with one rupee.\r<BR>\n" );
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document.write( "at the original price, he can get 34 oranges.\r<BR>\n" );
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document.write( "the numbers don't work out exactly because the 13.33% is a truncated version of 13.333333333333333333% which is equal to 200/15.\r<BR>\n" );
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document.write( "the decimal equivalent of that is 2/15 which is equivalent to .13333333333333.\r<BR>\n" );
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document.write( "if you used that number instead, then the numbers would have come out exactly.\r<BR>\n" );
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document.write( "if you were confused by the fact that the numbers didn't come out as integers, that's the reason.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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