document.write( "Question 1179761: The sum of two whole numbers is 29. find the maximum possible product of the two numbers. \n" ); document.write( "

Algebra.Com's Answer #809353 by ikleyn(52864) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " Surely, the answer by @mananth is incorrect: \r
\n" ); document.write( "\n" ); document.write( " the problem asks about INTEGER numbers, while his / (her) answer is non-integer.\r
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document.write( "If x is one number, then the other number is 29-x.\r\n" );
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document.write( "Their product is  x*(29-x) = 29x - x^2.    (1)\r\n" );
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document.write( "This function is a parabola placed downward.\r\n" );
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document.write( "    29x - x^2 = .    (2)\r\n" );
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document.write( "The parabola has the vertex at x = 14.5.\r\n" );
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document.write( "From the formula (2), it is clear, that our integer numbers are those that are closest to 14.5.\r\n" );
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document.write( "These numbers are 14 and 15.\r\n" );
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document.write( "So, there are two pairs of the numbers that give the answer:  (14,15)  and  (15,14).\r\n" );
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document.write( "Their product is  14*15 = 210 = 15*14.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
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