Question

The avg of a list of 4 numbers is 90. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 80, and the fourth number in the new list is 96. What is the avg of this new list of numbers?

I know the answer is 94 but do not know how to go about solving.

Answer 1

`94` indeed

Explanation:

`(a + b + c + 96)/4 = x`

`(a + b + c + 80)/4 = 90`

How much is a + b + c ?

`a + b + c + 80 = 360`

`a + b + c = 280`

`x = (280 + 96)/4 = 376/4 = 94`

Answer 2

See a solution process below:

Explanation:

If the average of the original list of 4 numbers is 90, then the sum of these 4 numbers is:

`4 xx 90 = 360`

If the 4th number in the original list is 80, then the sum of the first 3 numbers in the original list is:

`360 - 80 = 280`

If the first 3 numbers in the new list are the same as in the original list then the sum of these new first 3 numbers is also:

`280`

If the 4th number in the new list is 96 then the sum of the 4 numbers in the new list is:

`280 + 96 = 376`

Therefore, the average of the new list of 4 numbers is:

`376 -: 4 = 94`