document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142701>Question 1142701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer bought some sheep for Rs. 9000. If he had paid Rs. 100 less for each, he would have got 3 sheep more for the same money. How many sheep did he buy, when the rate in each case is same </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763409 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=763409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> he bought x number of sheep for 9000.<BR>\n" );
document.write( "the price per sheep is y.<BR>\n" );
document.write( "therefore x * y = 9000\r<BR>\n" );
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document.write( "if the price was 100 less, he could have bought 3 more sheep for the same money.<BR>\n" );
document.write( "the equation for that becomes (x + 3) * (y - 100) = 9000\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.<BR>\n" );
document.write( "they are:\r<BR>\n" );
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document.write( "x * y = 9000<BR>\n" );
document.write( "(x + 3) * (y - 100) = 9000\r<BR>\n" );
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document.write( "simplify these equations to get:\r<BR>\n" );
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document.write( "x * y = 9000<BR>\n" );
document.write( "x * y - 100 * x + 3 * y - 300 = 9000\r<BR>\n" );
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document.write( "replace x * y in the second equation with 9000 from the first equation to get:\r<BR>\n" );
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document.write( "9000 - 100 * x + 3 * y - 300 = 9000\r<BR>\n" );
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document.write( "the 9000 on both sides of the equation cancel out and you are left with:\r<BR>\n" );
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document.write( "-100 * x + 3 * y - 300 = 0\r<BR>\n" );
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document.write( "from the first equation of x * y = 9000, solve for y to get y = 9000 / x\r<BR>\n" );
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document.write( "in the second equation of -100 * x + 3 * y - 300 = 0, replace y with 9000 / x to get:\r<BR>\n" );
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document.write( "-100 * x + 3 * (9000 / x) - 300 = 0<BR>\n" );
document.write( "multiply both sides of this equation by x to get:<BR>\n" );
document.write( "-100 * x^2 + 27000 - 300 * x = 0<BR>\n" );
document.write( "reorder this equation in descending order of degree to get:<BR>\n" );
document.write( "-100 * x^2 - 300 * x + 27000 = 0<BR>\n" );
document.write( "divide both sides of this equation by -100 to get:<BR>\n" );
document.write( "x^2 + 3x - 270 = 0<BR>\n" );
document.write( "factor this equation to get (x + 18) * (x - 15) = 0<BR>\n" );
document.write( "solve for x to get x = -18 or x = 15<BR>\n" );
document.write( "x has to be positive, so x = 15 looks like a possible solution.\r<BR>\n" );
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document.write( "when x = 15, x * y = 9000 gets you y = 600.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "x * y = 15 * 600 = 9000<BR>\n" );
document.write( "(x + 3) * (y - 100) becomes 18 * 500 = 9000\r<BR>\n" );
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document.write( "solution is:<BR>\n" );
document.write( "he bought 15 sheep at 600 apiece for a total cost of 9000.<BR>\n" );
document.write( "if the price dropped 100 for each sheep, then he could have bought 18 sheep at 500 apiece for the same total cost of 9000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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