document.write( "Question 1118645: a set of six different positive integers has a median and mean of 6. if the largest number in the set is 12, what is the largest possible sum for the largest 3 numbers \n" ); document.write( "

Algebra.Com's Answer #734020 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "(1) If a set of 6 different positive integers has a median of 6, then the average of the 3rd and 4th numbers must be 6.

\n" ); document.write( "(2) We want the sum of the last three numbers to be as large as possible; that means the sum of the first three integers must be as small as possible.

\n" ); document.write( "So try 1, 2, 3 for the first three numbers. That means the 4th integer is 9; the first 4 numbers are now 1, 2, 3, 9.

\n" ); document.write( "Can we find two more numbers that satisfy all the conditions of the problem? The sum of all six integers must be 36; and the last two numbers must be larger than 9. The sum of the first four integers is 15; the sum of the last two must be 21.

\n" ); document.write( "AHA! 10 and 11 work perfectly!

\n" ); document.write( "The numbers we want are 1, 2, 3, 9, 10, 11.

\n" ); document.write( "To answer the specific question that was asked, the sum of the largest three integers is 9+10+11 = 30. \n" ); document.write( "

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