SOLUTION: The average of 16 consecutive positive integers is 30.5what is the average of the first 8 in the set?

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Question 1143828: The average of 16 consecutive positive integers is 30.5what is the average of the first 8 in the set?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Then the 8-th number is 30,

     the 7-th number is 29,

         6-th           28

         5-th           27

         4-th           26

         3-rd           25

         2-nd           24

         1-st           23


and the average of the first 8 numbers is    = 26.5.   ANSWER


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Consider the 16 consecutive integers with an average of 30.5 as two sets -- the largest 8 consecutive integers less than 30 and the smallest 8 consecutive integers greater than 30.

Each integer in the second set is 8 more than a corresponding number in the first set; that means the average of the numbers in the first set is 8 less than the average of the numbers in the second set.

Then, since the average of all the numbers is 30.5, the average of the numbers in the first set must be 26.5, and the average of the numbers in the second set must be 34.5.

ANSWER: 26.5
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