document.write( "Question 1010939: One number is 5 more than another. The difference between their squares is 105. What are the numbers? \n" ); document.write( "

Algebra.Com's Answer #626469 by ikleyn(52832) $\"\"$ $\"About$

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\n" ); document.write( "One number is 5 more than another. The difference between their squares is 105. What are the numbers?
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document.write( "Let x be the greater number, and let y be the smaller one.\r\n" );
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document.write( "Then we have two equations from the condition\r\n" );
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document.write( "x - y = 5,           (1)\r\n" );
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document.write( "and\r\n" );
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document.write( " = .     (2)\r\n" );
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document.write( "Factor (2):\r\n" );
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document.write( "(x-y)*(x+y) = 105.   (3)\r\n" );
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document.write( "Replace the first factor in (3) by 5, in accordance with (1). You will get\r\n" );
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document.write( "5*(x+y) = 105,   hence\r\n" );
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document.write( "x + y =  = 21.   (4)\r\n" );
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document.write( "Thus you have the system of two equations (1) and (4):\r\n" );
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document.write( "x - y = 5,   (1')   and\r\n" );
document.write( "x + y = 21.  (4')\r\n" );
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document.write( "Add (1') and (4'). You will get 2x = 26. Hence, x = 13.\r\n" );
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document.write( "Distract (1') from ((4'). You will get 2y = 16. Hence, y = 8.\r\n" );
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document.write( "Answer. x = 13, y = 8.\r\n" );
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