document.write( "Question 1142701: 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 \n" ); document.write( "

Algebra.Com's Answer #763410 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let \"  n \"  be the number of sheep.\r\n" );
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document.write( "Then from the condition you have this equation\r\n" );
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document.write( "     -  = 100.\r\n" );
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document.write( "Divide by 100 both sides. You will get\r\n" );
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document.write( "     -  = 1.\r\n" );
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document.write( "At this point, I just see a mental solution:  n= 15.\r\n" );
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document.write( "If you want to get a formal algebra solution, multiply both sides of the last equation by  n*(n+3)  and then simplify\r\n" );
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document.write( "    90*(n+3) - 90n = n*(n+3)\r\n" );
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document.write( "    90n + 270 - 90n = n^2 + 3n\r\n" );
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document.write( "    n^2 + 3n - 270 = 0\r\n" );
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document.write( "    (n-15)*(n+18) = 0.\r\n" );
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document.write( "Of the two roots  n=15  and  n= -18, only positive  15 is the solution to the problem.\r\n" );
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document.write( "ANSWER.  15 sheep.\r\n" );
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document.write( "CHECK.    -  = 600 - 500 = 100.    ! Correct !\r\n" );
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