document.write( "Question 1150417: A farmer bought a number of pigs for $150. However, 8 of them died before he could sell the rest at a profit of $6 per pig. His total profit was $92. How
\n" ); document.write( "many pigs did he originally buy? \n" ); document.write( "
Algebra.Com's Answer #771822 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
A farmer bought a number of pigs for $150. However, 8 of them died before he
\n" ); document.write( "could sell the rest at a profit of $6 per pig. His total profit was $92. How
\n" ); document.write( "many pigs did he originally buy?
\n" ); document.write( "
\r\n" );
document.write( "Suppose he originally bought N pigs for $150, so he paid $150/N per pig.  Then 8\r\n" );
document.write( "died, so he then had only N-8 pigs to sell.  He then sold N-8 pigs each for $6\r\n" );
document.write( "more than he paid, or $150/N + 6 each.  So he took in $[150/N + 6][N-8].  This was $92\r\n" );
document.write( "more than the $150 he paid, or $150+$92 or $242.  So the equation is\r\n" );
document.write( "\r\n" );
document.write( "$[150/N + 6][N-8] = $242\r\n" );
document.write( "\r\n" );
document.write( "[150/N + 6][N-8] = 242\r\n" );
document.write( "\r\n" );
document.write( "Clear the fraction by multiplying both sides by N\r\n" );
document.write( "\r\n" );
document.write( "N∙[150/N + 6][N-8] = N∙242\r\n" );
document.write( "\r\n" );
document.write( "[150 + 6N][N-8] = 242N\r\n" );
document.write( "\r\n" );
document.write( "150N-1200+6N²-48N = 242N\r\n" );
document.write( "\r\n" );
document.write( "6N²+102N-1200 = 242N \r\n" );
document.write( "\r\n" );
document.write( "6N²-140N-1200 = 0\r\n" );
document.write( "\r\n" );
document.write( "Divide all terms on both sides by 2\r\n" );
document.write( "\r\n" );
document.write( "3N²-70N-600 = 0\r\n" );
document.write( "\r\n" );
document.write( "(3N+20)(N-30) = 0\r\n" );
document.write( "\r\n" );
document.write( "3N+20=0; N-30=0\r\n" );
document.write( "\r\n" );
document.write( "3N=-20;   N=30\r\n" );
document.write( "\r\n" );
document.write( "    N=-20/3\r\n" );
document.write( "\r\n" );
document.write( "Ignore the negative fractional answer.\r\n" );
document.write( "\r\n" );
document.write( "Solution: 30 pigs\r\n" );
document.write( "\r\n" );
document.write( "Let's check:\r\n" );
document.write( "\r\n" );
document.write( "He bought 30 pigs for $150. So he paid $150/30 = $5 per pig.  Then 8 died.  So\r\n" );
document.write( "he only had 22 pigs to sell. He sold each of the 22 pigs for $6 more than he\r\n" );
document.write( "paid, so he sold each pig for $11. Since he sold 22 pigs, he ended up with\r\n" );
document.write( "22∙$11 = $242, and since he paid $150 for the pigs in the beginning, his profit\r\n" );
document.write( "was $242-$150 = $92.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );