document.write( "Question 1163463: A market woman purchased a number of plates for GH¢ 150.00. Four the plates got broken while transporting them to her shop. By selling the remaining plates at a profit of GH¢ 1.00 on each, she made a total profit of GH¢ 6.00. How many plates did she purchase?\r
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Algebra.Com's Answer #787561 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "A market woman purchased a number of plates for GH¢ 150.00. Four the plates got broken while transporting them to her shop.
\n" ); document.write( "By selling the remaining plates at a profit of GH¢ 1.00 on each, she made a total profit of GH¢ 6.00. How many plates did she purchase?
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document.write( "Let n be the number of plates she purchased.\r\n" );
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document.write( "Then the price she paid for each plate while purchased is    money units.\r\n" );
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document.write( "She then sold (n-4) plates for 150+6 = 156 money units, so her price while selling was  .\r\n" );
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document.write( "The difference of prices was 1 money unit, according to the condition.\r\n" );
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document.write( "It gives you an equation\r\n" );
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document.write( "     -  = 1.\r\n" );
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document.write( "It is your base equation.\r\n" );
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document.write( "To solve it, multiply both sides by n*(n-4).  You will get then\r\n" );
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document.write( "    156n - 150*(n-4) = n*(n-4).\r\n" );
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document.write( "Simplifying, you get\r\n" );
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document.write( "    n^2 - 10n - 600 = 0.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (n-30)*(n+20) = 0.\r\n" );
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document.write( "Of two roots, 30 and -20, only positive value n= 30 is the solution to the problem.\r\n" );
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document.write( "ANSWER.  30 plates.\r\n" );
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document.write( "CHECK.   -  =  -  = 6 - 5 = 1 money unit.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "If after reading my post you will have questions, do not hesitate to post them to me.\r
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\n" ); document.write( "\n" ); document.write( "If you do, then please refer to the ID number of this problem, which is 1163463.\r
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\n" ); document.write( "\n" ); document.write( "The ID number is the first number, which you see in your page in the UPPER LEFT corner.\r
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\n" ); document.write( "\n" ); document.write( "If you will post to me without referring to this ID number, I will not know to whom to answer.\r
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\n" ); document.write( "\n" ); document.write( "It is how this forum works.\r
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\n" ); document.write( "\n" ); document.write( "So, mentioning this ID is NECESSARY, if you want to have two-way communication with me.\r
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