Following clues describe a list of 5 integers. What is the greatest of the number in the list?
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document.write( "clue 1-two of the numbers are negative
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document.write( "clue 2-the median value is 8, the mean is 18.6 and the range is 60
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document.write( "clue 3-one of the numbers is a perfect square, andone of the numbers is one more than a perfect square
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document.write( "clue 4-the difference between the least two integers is 6
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document.write( "I'm stuck
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document.write( "Let the five numbers be A,B,C,D,E where A ≦ B ≦ C ≦ D ≦ E.\r\n" );
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document.write( "clue 2-the median value is 8,
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document.write( "For a set of 5 numbers (or any odd number of numbers), \r\n" );
document.write( "the median is the middle number when they are listed\r\n" );
document.write( "smallest to largest.\r\n" );
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document.write( "so we have C = 8, and we now have:\r\n" );
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document.write( " A ≦ B ≦ 8 ≦ D ≦ E\r\n" );
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document.write( "clue 1-two of the numbers are negative
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document.write( "Those have to be A and B. So we can insert 0 in between the B and the 8.\r\n" );
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document.write( " A ≦ B < 0 < 8 ≦ D ≦ E \r\n" );
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document.write( "clue 4-the difference between the least two integers is 6
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document.write( "The two negative ones have to be the least two, which are A and B.\r\n" );
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document.write( "That means B - A = 6 or \r\n" );
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document.write( "(1) B = A+6, \r\n" );
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document.write( "so replacing B by A+6 we have:\r\n" );
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document.write( " A < A+6 < 0 < 8 ≦ D ≦ E\r\n" );
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document.write( "...the mean is 18.6
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document.write( " So we add them up, divide by 5 and that must equal 18.6:\r\n" );
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document.write( "Multiply through by 5 to clear of fractions.\r\n" );
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document.write( "2A+14+D+E = 18.6×5 = \r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "2A+14+D+E = 93\r\n" );
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document.write( "(2) 2A+D+E = 79 \r\n" );
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document.write( "and the range is 60, so\r\n" );
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document.write( "E-A = 60, or\r\n" );
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document.write( "(3) E-60 = A\r\n" );
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document.write( "Use (3) to substitute E-60 for A in (2)\r\n" );
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document.write( "(2) 2A+D+E = 79\r\n" );
document.write( " 2(E-60)+D+E = 79\r\n" );
document.write( " 2E-120+D+E = 79\r\n" );
document.write( " 3E+D = 199\r\n" );
document.write( "(4) D = 199-3E \r\n" );
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document.write( "We know that D must be 8 or larger, so\r\n" );
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document.write( " D ≧ 8\r\n" );
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document.write( "Use (4) to substitute 199-3E for D\r\n" );
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document.write( " 199-3E ≧ 8\r\n" );
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document.write( "Solve for E\r\n" );
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document.write( " -3E ≧ -191\r\n" );
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document.write( "Dividing through by a negative number, -3, reverses the inequality:\r\n" );
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document.write( " E ≦ 
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document.write( "Clue 3-one of the numbers is a perfect square, andone of the numbers is one more than a perfect square
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document.write( "So one of D and E is a perfect square and the other is one more than\r\n" );
document.write( "a perfect square. So we try perfect squares and 1 more than perfect\r\n" );
document.write( "squares less than and larger than 8, for D and E.\r\n" );
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document.write( "perfect squares: 9, 16, 25, 36, 49\r\n" );
document.write( "perfect squares plus1: 10, 17, 26, 37, 50 \r\n" );
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document.write( "Let's try D = 49 in (4)\r\n" );
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document.write( " D = 199-3E \r\n" );
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document.write( " 49 = 199-3E\r\n" );
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document.write( " 3E = 150\r\n" );
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document.write( " E = 50\r\n" );
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document.write( "and E=50 is one of those \"perfect square + 1's, namely 1 more than 49, or D.\r\n" );
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document.write( "So I think we have it.\r\n" );
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document.write( "Substitute D = 49 and E = 50 in (2)\r\n" );
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document.write( " (2) E-60 = A\r\n" );
document.write( " 50-60 = A\r\n" );
document.write( " -10 = A \r\n" );
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document.write( "and substituting in (1)\r\n" );
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document.write( " B = A+6\r\n" );
document.write( " B = -10 + 6\r\n" );
document.write( " B = -4.\r\n" );
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document.write( "So the numbers are\r\n" );
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document.write( "A = -10, B = -4, C = 8, D = 49, E = 50.\r\n" );
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document.write( "Edwin
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