document.write( "Question 1198817: The members of a club decide to buy a cassette tape recorder worth sh. 3000.00 by contributing equal amounts of money. Ten members fail to honour to their commitment and each of the rest then has to raise sh. 10 more. Find the number of people in the club \n" ); document.write( "

Algebra.Com's Answer #832466 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "The members of a club decide to buy a cassette tape recorder worth sh. 3000.00
\n" ); document.write( "by contributing equal amounts of money. Ten members fail to honour to their commitment
\n" ); document.write( "and each of the rest then has to raise sh. 10 more. Find the number of people in the club
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document.write( "Let n be the number of members.\r\n" );
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document.write( "Then you have this equation from the problem\r\n" );
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document.write( "     -  = 10,\r\n" );
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document.write( "or, reducing the factor 10 in both sides\r\n" );
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document.write( "     -  = 1.\r\n" );
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document.write( "At this point, you may GUESS the solution: n= 60,\r\n" );
document.write( "or you may to solve this equation formally.\r\n" );
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document.write( "To solve it formally, multiply both sides by n*(n-10), then simplify\r\n" );
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document.write( "    300n - 300*(n-10) = n*(n-10)\r\n" );
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document.write( "          3000        = n*(n-10)\r\n" );
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document.write( "    n^2 - 10n - 3000 = 0\r\n" );
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document.write( "    (n-60)*(n+50) = 0    \r\n" );
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document.write( "Of the two roots, 60 and -50, you choose (naturally) the positive value.\r\n" );
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document.write( "ANSWER.  There are 60 members in the club.\r\n" );
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