The average of a list of integers goes up by 2 when 23 is added to the list. if 9 is added to the new list, then the average reduces by 1. how many integers were there in the original list?

There were 4 numbers in the original integer list.

Step-by-step explanation:

Suppose that x is the sum of the integers in the original list, n is the number of integers in the original list and y is the average of those integers. The next formula represents the average of the numbers:

From this equation, you can tell that x=ny.  

The problem gives us the following information:  

1. The average of a list of integers goes up by 2 when 23 is added to the list, the next equation describes this situation (call this equation Eq 1)

2. If 9 is added to the new list, then the average reduces by 1, the next equation describes this situation, you have to add 2 to n (call this equation Eq 2)

Now, use the fact that x=ny and replace it in both equations, the new equations will be:

Eq 1:

Eq 2:

Solve y in Eq 1:

Replace y in Eq 2:

The number of integers in the original list (n) was 4.

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