document.write( "Question 1208330: Hi
\n" ); document.write( "If Bob sells a TV at a discount of 15% of the marked price he will make a profit of $135. If he sells at a discount of 25% of marked price he makes a loss of $65. What is the cost price of the TV. \n" ); document.write( "

Algebra.Com's Answer #846692 by ikleyn(52780) $\"\"$ $\"About$

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\n" ); document.write( "If Bob sells a TV at a discount of 15% of the marked price he will make a profit of $135.
\n" ); document.write( "If he sells at a discount of 25% of marked price he makes a loss of $65.
\n" ); document.write( "What is the cost price of the TV.
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\n" ); document.write( "\n" ); document.write( " By the definition, \" cost price \" is the amount of money that is spent to produce \r
\n" ); document.write( "\n" ); document.write( " goods or services before any profit is added for the manufacturer or producer.\r
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document.write( "Let X be the cost price in this problem.\r\n" );
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document.write( "Let Y be the selling price in this problem (same as the marked price).\r\n" );
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document.write( "From the first statement of the problem, we have this equation\r\n" );
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document.write( "    (1-0.15)Y - X = 135  dollars   (1)     (profit)\r\n" );
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document.write( "From the second statement of this problem, we have second equation\r\n" );
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document.write( "    (1-0.25)Y - X = -65  dollars    (2)    (loss)\r\n" );
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document.write( "So, we have a system of two equations, which I will write in the form\r\n" );
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document.write( "    0.85Y - X = 135    (1')\r\n" );
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document.write( "    0.75Y - X = -65    (2')\r\n" );
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document.write( "To solve it, subtract equation (2') from equation (1').  You will get\r\n" );
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document.write( "    0.85Y - 0,75Y = 135 - (-65),\r\n" );
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document.write( "    0.1Y = 200,\r\n" );
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document.write( "       Y = 200/0.1 = 2000.\r\n" );
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document.write( "To find X, substitute Y = 2000 into equation (1')\r\n" );
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document.write( "    0.85*2000 - X = 135,\r\n" );
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document.write( "    0.85*2000 - 135 = X,\r\n" );
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document.write( "          1565      = X,\r\n" );
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document.write( "             X      = 1565. \r\n" );
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document.write( "ANSWER.  The cost price is $1565.\r\n" );
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