document.write( "Question 1189179: The sum of two numbers is 25. The sum of their reciprocals is 1/4. Determine the two numbers. \n" ); document.write( "

Algebra.Com's Answer #820451 by ikleyn(53765) $\"\"$ $\"About$

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\n" ); document.write( "The sum of two numbers is 25. The sum of their reciprocals is 1/4. Determine the two numbers.
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document.write( "Your starting equations are\r\n" );
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document.write( "    x + y = 25           (1)\r\n" );
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document.write( "     +  =         (2)\r\n" );
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document.write( "From equation (2)\r\n" );
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document.write( "    4*(x+y) = xy\r\n" );
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document.write( "Replace here x+y by 25, based on equation (1).  You will get\r\n" );
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document.write( "    xy = 4*25 = 100.\r\n" );
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document.write( "So, you have two equations\r\n" );
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document.write( "    x + y = 25       (3)\r\n" );
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document.write( "     xy   = 100      (4)\r\n" );
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document.write( "From here, the  ANSWER  is OBVIOUS:  (x,y) = (20,5)  or  (5,20).      (*)\r\n" );
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document.write( "If you want to get formal solution, express  x = 25-y from (3) and substitute it to (4).  You will get\r\n" );
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document.write( "    (25-y)*y = 100\r\n" );
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document.write( "    25y - y^2 = 100\r\n" );
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document.write( "    y^2 - 25y + 100 = o\r\n" );
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document.write( "    (y-20)*(y-5) = 0\r\n" );
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document.write( "giving two possibilities  y= 20  or  y= 5.\r\n" );
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document.write( "They lead to answer (*): the numbers are 5 and 20, in any order.\r\n" );
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