Question 999015
there are an infinite list of 6 numbers that will give you an average of 78, if the numbers can be allowed to be both positive or negative.


if the numbers can only be positive, then there is a finite set.


average = total / number of items


this formula becomes:


78 = total / 6


solve for total to get total = 6 * 78 = 468.


all you need to do is find 6 numbers that add up to 468.


here's a couple of examples:


78,78,78,78,78,78


1,1,1,1,1,465


1,2,3,4,5,453


the only requirement is that the sum of the numbers is equal to 468.


that's because the average is then 78, because 468 / 6 = 78.


withouot any restriction as to whether the numbers have to be positive or negative, here's all you need to do.


pick any 5 numbers.
doesn't matter what they are.


for example:


1, 307, 523, 798, 1500, x


the 6th number is x, because you don't know what it is just yet.


you want to solve for x.


add up the 5 numbers you already know to get:


3129 + x = 468


the sum of the numbers has to be 468.


solve for x to get x = 468 - 3129 = -2661.


your 6th number is -2661.


you get:


1 + 307 + 523 + 798 + 1500 + x = 468 becomes:


1 + 307 + 523 + 798 + 1500 - 2661 = 468


the sum is 468, as it should be.


468 / 6 = an average of 78.


you can pick any 5 numbers, but the 6th one is determined by what the total needs to be.


you were not given any restrictions, so the 6th number can be negative or positive.


so, pick any 5 numbers.


add them up.


let x be the 6th number.


the sum of the 5 numbers + x has to be equal to 468.


solve for x.


when you add up the 5 numbers plus the value for x that you solved for, you get the total that will be 468, and when you divide 468 by 6, you will get 78 as the average.