document.write( "Question 1152383: a shop owner orders a number of drinking glasses which she pays R300, while unpacking the glasses, 10 get broken she decide to sell each remaining glasses at R4 more than she paid for them . she manages to make a profit of R100 on the transaction. how many glasses did she initially order and what was the price the price of each? \n" ); document.write( "

Algebra.Com's Answer #774401 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Let x be the value under the question (the original number of glasses).\r\n" );
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document.write( "Then the price for each glass when buying is   rupees.\r\n" );
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document.write( "She made R100 profit selling, so she sold for R300 + R100 = R400.\r\n" );
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document.write( "The number of glasses sold is (x-10), according to the condition.\r\n" );
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document.write( "For each of (x-10) glasses sold, she get R4 more than paid per glass buying.\r\n" );
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document.write( "It means that\r\n" );
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document.write( "     -  = 4.    (1)\r\n" );
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document.write( "It is your basic equation.\r\n" );
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document.write( "To solve it, multiply both sides by x*(x-10).  You will get\r\n" );
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document.write( "    400x - 300*(x-10) = 4x*(x-10).\r\n" );
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document.write( "Simplify step by step and solve\r\n" );
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document.write( "    400x - 300x + 3000 = 4x^2 - 40x\r\n" );
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document.write( "    4x^2 -40x - 100x - 3000 = 0\r\n" );
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document.write( "    4x^2 - 140x - 3000 = 0\r\n" );
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document.write( "     x^2 - 35x - 750 = 0\r\n" );
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document.write( "    (x-50)*(x+15) = 0  \r\n" );
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document.write( "Of the two roots, 50 and -15, only positive value x= 50 is the solution.\r\n" );
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document.write( "ANSWER.  50 glasses were bought at the price of   = R6.\r\n" );
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document.write( "CHECK.  I will check that the equation (1) is valid.\r\n" );
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document.write( "         -  =  -  = 10 - 6 = 4.    ! Precisely correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems and to learn THE METHOD, look into my lessons\r
\n" ); document.write( "\n" ); document.write( " - Challenging word problems solved using quadratic equations \r
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