SOLUTION: In a set of counting numbers, all have different values. Their sum is 350. Their average is 50. One of the numbers is 100. What is the greatest number that can be in the set ? B

Question 1015318: In a set of counting numbers, all have different values. Their sum is 350. Their average is 50. One of the numbers is 100. What is the greatest number that can be in the set ?
Based on average and sum, I could confirm that there are 7 seven numbers. What next ??

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you want the other numbers to be as small as possible.
assuming the first number is 1 (the set of counting numbers is positive integers only not including 0), than you can get 1,2,3,4,5,6 + the 7th number.
since the total has to be 350, then just subtract the sum of the first 6 numbers and that's your 7th number.
the sum of 1,2,3,4,5,6 = 21.
350 - 21 = 329.
329 should be the largest number you can have.
329 + 21 = 350 / 7 = average of 50.

if 100 has to be one of the numbers, then replace 6 with 100 and you get:
1,2,3,4,5,100 + the 7th number.
the sum of the first 6 number is now 115.
the 7th number has to be 350 - 115 = 235.
the 7 number are now 1,2,3,4,5,100,235.
the total is 350 / 7 = average of 50.

235 is now the biggest number that can be in the set.

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