+816 For a certain set of five numbers, the mean of all but the largest number is 80, and the mean of all but the smallest number is 90. What is the range of the set of five numbers?
+4609 First, we know that mean=sum of numbers/number of numbers.
Since the question gave us that the mean of all the numbers but the largest number is 80, we can do: \(80*(5-1)=80*4=320+x\)
Also, the question gave us that the mean of all but the smallest number is 90, so we can do:
\(90*(5-1)=90*4=360+y\)
Translating this into math language, by making both equal, we have: \(320+x=360+y\)
Taking \(y\) to the other side and \(320\) to the other side, we have: \(x-y=360-320\)
Finishing this off, we get: \(x-y=\boxed{40}\)
The range is greatest-least, so the above answer is correct.
