SOLUTION: The average of a set of n numbers is 23. When -35 is added to the set, the average is 21. How many numbers were in the original set?

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Question 1149394: The average of a set of n numbers is 23. When -35 is added to the set, the average is 21. How many numbers were in the original set?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Let x be the number of numbers in the original set.

Since the average of the numbers is 23, the sum of the numbers in that set is 23x.

When the number -35 is added to the original set, we end up with a set of (x+1) numbers with an average of 21.

The sum of the numbers in the new set can be written in two different ways:

(1) 23x-35 (the sum of the numbers in the original set, plus the one added number)
(2) 21(x+1) (the sum of (x+1) numbers with an average of 21)

So



Solve using basic algebra....
Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.

23*n - 35 = 21*(n+1).


23n - 21n = 35 + 21


2n = 56


n =  = 28.   ANSWER


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