document.write( "Question 831094: four integers are added to a group of integers 3,4,5,5 and 8 and the mean, median and mode are increased by 1 each. what is the greatest integer in the new group of integers \n" ); document.write( "
Algebra.Com's Answer #501148 by JulietG(1812)\"\" \"About 
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Existing integers: 3,4,5,5,8
\n" ); document.write( "Mean for those integers = 25/5 = 5
\n" ); document.write( "Mode for those integers = 5 (occurring most often)
\n" ); document.write( "Median for those integers = 5 (which number in the middle?)
\n" ); document.write( ".
\n" ); document.write( "Where we want to be is:
\n" ); document.write( "Mean = (25 + A,B,C,D)/9 = 6
\n" ); document.write( "Mode = 6
\n" ); document.write( "Median = 6
\n" ); document.write( ".
\n" ); document.write( "What helps most here is the mode. Since 5 occurs twice, 6 will necessarily have to be 3 of the remaining numbers. Now all we have to figure out is the 4th one.
\n" ); document.write( ".
\n" ); document.write( "Knowing that 3 of the new numbers are 6, here's what we then have:
\n" ); document.write( "Mean = (43 + D)/9 = 6 [43 is 25 +6+6+6]
\n" ); document.write( "We can find the fourth number with this equation.
\n" ); document.write( "Let's multiply each side by 9 to get rid of that pesky fraction
\n" ); document.write( "43+D = 6*9
\n" ); document.write( "43+D = 54
\n" ); document.write( "subtract 43 from each side to get
\n" ); document.write( "D = 11
\n" ); document.write( ".
\n" ); document.write( "Let's put out new four numbers in to make certain they're correct: 6,6,6,11
\n" ); document.write( "New set: 3,4,5,5,6,6,6,8,11
\n" ); document.write( "Mean = total values divided by number of values. 3+4+5+5+6+6+6+8+11 = 54. 54/9 = 6
\n" ); document.write( "Median -- which number is in the middle? 6
\n" ); document.write( "Mode -- which number occurs most often? 6
\n" ); document.write( "Success! \n" ); document.write( "
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