document.write( "Question 1043768: The difference between two integers is 5. If the reciprocal of the smaller is added to twice the reciprocal of the larger the result is 23/66. Find the two integers. \n" ); document.write( "

Algebra.Com's Answer #658934 by Edwin McCravy(20067) $\"\"$ $\"About$

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document.write( "Let y = the larger integer\r\n" );
document.write( "Let x = the smaller integer\r\n" );
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document.write( "Substitute (5+x) for y in\r\n" );
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document.write( "LCD = 66x(5+x)\r\n" );
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document.write( "Multiply each numerator by every factor of\r\n" );
document.write( "the denominator which is not under it:\r\n" );
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document.write( "Subtract 115x from both sides\r\n" );
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document.write( "Subtract 23x² from both sides\r\n" );
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document.write( "to get 0 on the right side\r\n" );
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document.write( "Arrange left side in descending order:\r\n" );
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document.write( "Multiply through by -1:\r\n" );
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document.write( "There may be a way to factor that but\r\n" );
document.write( "when the numbers are that big, it's\r\n" );
document.write( "easier to use the quadratic formula,\r\n" );
document.write( "especially if you have a calculator:\r\n" );
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document.write( "Using the +\r\n" );
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document.write( "Using the -\r\n" );
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document.write( "The problem calls for an integer.  That's not\r\n" );
document.write( "an integer, so we can discard that value of x.\r\n" );
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document.write( "So x = 6\r\n" );
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document.write( "Substitute into\r\n" );
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document.write( "Answers: Larger integer = 11, Smaller integer = 6\r\n" );
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document.write( "Edwin

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