document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1038295>Question 1038295</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer bought a number of pigs for $145. However, 8 of them died before he could sell the rest at a profit of 2 per pig. His total profit was $2. How many pigs did he originally buy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652995 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=652995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there's an easy way to solve this.<BR>\n" );
document.write( "since the number of pigs has to be an integer, then look for all the factors of 145.<BR>\n" );
document.write( "you get 1 * 147 or 5 * 29 and i think nothing else.<BR>\n" );
document.write( "it can't be 1 and it can't be 5 so it has to be either 147 or 29.<BR>\n" );
document.write( "i went for 29 and got good results.<BR>\n" );
document.write( "with 29 pigs bought, the cost per pig is 5 dollars.<BR>\n" );
document.write( "8 pigs died, so 21 pigs were sold at a profit of 2 dollars apiece.<BR>\n" );
document.write( "this means they were sold for 7 dollar each.<BR>\n" );
document.write( "total revenue was 21 * 7 = 147 dollars.<BR>\n" );
document.write( "total profit was 2 dollars.<BR>\n" );
document.write( "solution looks good.\r<BR>\n" );
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document.write( "i had a lot more trouble solving it algebraically.<BR>\n" );
document.write( "i finally latched on to a method that provided the algebraic solution.\r<BR>\n" );
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document.write( "let x = the number of pigs.<BR>\n" );
document.write( "let c - the cost per pig.\r<BR>\n" );
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document.write( "since the total cost is 145, you get x*c = 145.\r<BR>\n" );
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document.write( "8 pigs died, so there were 21 pigs left.<BR>\n" );
document.write( "these were sold at a profit of 2 dollars apiece.<BR>\n" );
document.write( "the total profit was 2 dollars.\r<BR>\n" );
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document.write( "you get (x-8) * (c+2) = 147\r<BR>\n" );
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document.write( "since the cost per pig was c, then the revenue per pig had to be c+2 in order to get a profit of 2 dollars per pig.\r<BR>\n" );
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document.write( "the number of pigs sold was x-8.\r<BR>\n" );
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document.write( "since the total profit was 2 dollars, then the total revenue had to be 147 dollars because the total cost was 145 dollars.\r<BR>\n" );
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document.write( "the two equations you have are:\r<BR>\n" );
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document.write( "x*c = 145<BR>\n" );
document.write( "(x-8) * (c+2) = 147\r<BR>\n" );
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document.write( "in the first equation, solve for c to get c = 145/x.\r<BR>\n" );
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document.write( "in the second equation, replace c with 145/x to get:\r<BR>\n" );
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document.write( "(x-8) * (c+2) = 147 becomes (x-8) * (145/x + 2) = 147\r<BR>\n" );
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document.write( "simplify by performing the multiplication to get 145 + 2x - (8*145)/x - 16 = 147\r<BR>\n" );
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document.write( "subtract 145 and add 16 to both sides of the equation to get 2x - (8*145)/x = 18\r<BR>\n" );
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document.write( "multiply both sides of this equation by x to get 2x^2 - (8*145) = 18x\r<BR>\n" );
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document.write( "subtract 18x from both sides of this equation and simplify 8*145 to get 2x^2 - 18x - 1160 = 0\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get x^2 - 9x - 580 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get (x-29) * (x+20) = 0\r<BR>\n" );
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document.write( "solve for x to get x = 29 or x = -20.\r<BR>\n" );
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document.write( "since the number of pigs can't be negative, then x = -20 is no good and your only valid solution is x = 29.\r<BR>\n" );
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document.write( "when x = 29, the total cost per pig is 145/29 = 5 dollars.<BR>\n" );
document.write( "a profit of 2 dollars per pig sold means each pig that was sold brought in 7 dollars.<BR>\n" );
document.write( "21 * 7 = 147.<BR>\n" );
document.write( "the total revenue was 147 and the total cost was 145 which made the total profit equal to 2 dollars.\r<BR>\n" );
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document.write( "the solution is confirmed to be good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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