document.write( "Question 1208367: Hi
\n" ); document.write( "If Simon gave 30% of his sweets to Terry they will have the same number of sweets. If Simon gave 250 sweets to Terry, Terry will 80% more sweets than Simon. How many sweets does Simon have. \n" ); document.write( "

Algebra.Com's Answer #846747 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "If Simon gave 30% of his sweets to Terry they will have the same number of sweets.
\n" ); document.write( "If Simon gave 250 sweets to Terry, Terry will 80% more sweets than Simon.
\n" ); document.write( "How many sweets does Simon have.
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document.write( "x = # of Simon' sweets;\r\n" );
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document.write( "y = # of Terry' sweets.\r\n" );
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document.write( "From the problem, we have two equations.\r\n" );
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document.write( "First equation is\r\n" );
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document.write( "    (1-0.3)x = y + 0.3x   (first statement),\r\n" );
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document.write( "which  simplifies to\r\n" );
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document.write( "    0.7x = y + 0.3x  --->  0.7x - 0.3x = y  --->  0.4x = y.\r\n" );
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document.write( "Second equation is\r\n" );
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document.write( "    x - 250 = = (y + 250) - 0.8*(x-250)  (second statement),\r\n" );
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document.write( "which  simplifies to\r\n" );
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document.write( "    x - 250 = y + 250  - 0.8x + 200,\r\n" );
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document.write( "    x - 250 - 250 - 200 = y - 0.8x\r\n" );
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document.write( "    x - 700 = y - 0.8x\r\n" );
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document.write( "    y = 1.8x - 700.\r\n" );
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document.write( "    \r\n" );
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document.write( "So, we have this system of two equations\r\n" );
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document.write( "    y = 0.4x             (1)\r\n" );
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document.write( "    y = 1.8x - 700       (2)\r\n" );
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document.write( "Equations  (1) and (2) have left sides identical, so their right sides are equal\r\n" );
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document.write( "    0.4x = 1.8x - 700\r\n" );
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document.write( "    700 = 1.4x \r\n" );
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document.write( "    x = 700/1.4 = 500.\r\n" );
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document.write( "Thus Simon has 500 sweets.\r\n" );
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document.write( "From equation (1), Terry has 0.4*x = 0.4*500 = 200 sweets.\r\n" );
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document.write( "ANSWER.  Simon has 500 sweets.\r\n" );
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