document.write( "Question 46085: Hello,\r
\n" ); document.write( "\n" ); document.write( "I could really use help with this problem:\r
\n" ); document.write( "\n" ); document.write( "The product of two numbers is 20, and the sum of their reciprocals is 3/5. Find the numbers. \r
\n" ); document.write( "\n" ); document.write( "Thank you in advance,
\n" ); document.write( "Louis \n" ); document.write( "

Algebra.Com's Answer #30596 by atif.muhammad(135) $\"\"$ $\"About$

You can put this solution on YOUR website!

The product of two numbers is 20, and the sum of their reciprocals is 3/5. Find the numbers.\r\n" );
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document.write( "Let one number be x, and the other be y.\r\n" );
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document.write( "Product of two numbers = 20\r\n" );
document.write( "x * y = 20\r\n" );
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document.write( "xy = 20\r\n" );
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document.write( "Sum of their reciprocals = 3/5\r\n" );
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document.write( "Through cross multiplication: \r\n" );
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document.write( "Through substituting xy for 20 (see above, xy=20)\r\n" );
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document.write( "x+y = 12\r\n" );
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document.write( "Now we have a pair of simultaneous equations:\r\n" );
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document.write( "xy = 20 .........(1)\r\n" );
document.write( "x+y = 12 .......(2)\r\n" );
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document.write( "Manipulate (2)\r\n" );
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document.write( "x +y = 12\r\n" );
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document.write( "y = 12 -x ..........(3)\r\n" );
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document.write( "Substitute (3) into (1):\r\n" );
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document.write( "xy = 20\r\n" );
document.write( "x(12-x) = 20\r\n" );
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document.write( "12x - x^2 = 20\r\n" );
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document.write( "x^2 -12x +20 = 0\r\n" );
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document.write( "Through factorisation (x-10)(x-2) = 0. Hence, x= 10 or 2\r\n" );
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document.write( "Substitute x=10 or 2 into (3)\r\n" );
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document.write( "y = 12-x\r\n" );
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document.write( "If x = 10, y = 12-10 = 2\r\n" );
document.write( "If x = 2,  y = 12-2 = 10\r\n" );
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document.write( "So we have two numbers, 10 and 2.\r\n" );
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