Question 999015: Please help me I don't know what to do the question is list 6 numbers with a average of 78 thank you for helping
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! Pick any numbers which work. You already know that  will work, but you should find six NON-IDENTICAL numbers which will work. You could pick six numbers and allow either ONE or NONE of them to be 78.
This is open to several different possible solutions. YOU FIND one of them.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! 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.
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