document.write( "Question 1200643: The sum of a number and three times another number is 30. Their product is a maximum. Determine the two numbers
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Algebra.Com's Answer #834816 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let \"another\" number be x.\r\n" );
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document.write( "Then \"the number\" is 30-3x.\r\n" );
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document.write( "The product of the two numbers is  x*(30-3x) = 3x*(10-x).\r\n" );
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document.write( "It is a quadratic function, represented by a parabola opened downward. Its roots (the x-intercepts) are 0 and 10.\r\n" );
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document.write( "The maximum is reached at the mid-point between the roots.\r\n" );
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document.write( "This mid-point is x= 5.\r\n" );
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document.write( "Thus \"another\" number is 5 and \"the number\" is 30-3*5 = 15.\r\n" );
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document.write( "ANSWER.  The number is 15.  Another number is 5.\r\n" );
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