document.write( "Question 1023723: You drive at an average speed of 50mph to a discount shopping mall, spend two hours shopping, and then return at an average speed of 25mph. The entire trip take 8 hours. How far away is the shopping mall? \n" ); document.write( "

Algebra.Com's Answer #639183 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "The sum of two numbers is 9 and the difference of their squares is 9. Find the numbers.?
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document.write( "x + y = 9,        (1)\r\n" );
document.write( " = 9.      (2)\r\n" );
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document.write( "Rewrite (2) in the form\r\n" );
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document.write( "(x+y)*(x-y) = 9,\r\n" );
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document.write( "then replace (x+y) by 9, due to (1). You will get\r\n" );
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document.write( "9*(x-y) = 9.\r\n" );
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document.write( "Next, reduce both sides by the factor 9. You will get\r\n" );
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document.write( "x - y = 1.        (3)\r\n" );
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document.write( "Now, you have thwo equations to solve,\r\n" );
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document.write( "x + y = 9,        (1')\r\n" );
document.write( "x - y = 1.        (3')\r\n" );
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document.write( "Add them. You will get 2x = 9 + 10  --->  2x = 10  --->  x =  = 5.\r\n" );
document.write( "Then from (1')  y = 9 - x = 9 - 5 = 4.\r\n" );
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document.write( "Answer.  x = 5, y = 4.\r\n" );
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