document.write( "Question 472883: If S is a set of 5 positive, distinct integers with an average (arithmetic mean) of 9 and a median of 7, what is the least possible value of the largest number in the set? \n" ); document.write( "
Algebra.Com's Answer #324231 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Let the numbers be \r\n" );
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document.write( "A, B, C, D, E \r\n" );
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document.write( "from smallest to largest, i.e., A < B < C < D < E\r\n" );
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document.write( "We want E to be smallest possible.\r\n" );
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document.write( "\"%28A%2BB%2BC%2BD%2BE%29%2F5\" = 9\r\n" );
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document.write( "Multiply through by 5\r\n" );
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document.write( "A + B + C + D + E = 45\r\n" );
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document.write( "Since the median is 7,  C = 7\r\n" );
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document.write( "A + B + 7 + D + E = 45\r\n" );
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document.write( "To make E the smallest, we have to make A and B\r\n" );
document.write( "as large as possible. But they have to be less\r\n" );
document.write( "than median C = 7. So we choose A = 5 and B = 6.\r\n" );
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document.write( "5 + 6 + 7 + D + E = 45\r\n" );
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document.write( "18 + D + E = 45\r\n" );
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document.write( "         E =  27 - D\r\n" );
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document.write( "E is smallest possible when D is the largest possible,\r\n" );
document.write( "so that we subtract the most possible from 27:\r\n" );
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document.write( "But  E > D, or\r\n" );
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document.write( "27 - D > D\r\n" );
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document.write( "    27 > 2D\r\n" );
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document.write( "  13.5 > D\r\n" );
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document.write( "So D is the largest value posible when D = 13\r\n" );
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document.write( "So E is smallest when E = 27 - 13 = 14\r\n" );
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document.write( "The 5 numbers are\r\n" );
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document.write( "5, 6, 7, 13, 14.\r\n" );
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document.write( "and 14 is the least possible value for the \r\n" );
document.write( "largest number in the set.\r\n" );
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document.write( "Edwin
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