Four positive integers, not necessarily different and each less than 100, have an average of 94. Determine a minimum possible value for one of these numbers

Question

Four positive integers, not necessarily different and each less than 100, have an average of 94. Determine a minimum possible value for one of these numbers

Answer 1

Hi Sasha,

 

The easiest way to think about a problem like this is to test the limits the problem gives you. For example, it tells us that the four numbers are positive integers - this tells us that the absolute minimum value of any of the numbers would be 1. But, it also tells us that they're all less than 100 - this tells us that the maximum value of any of the numbers must be 99. They wouldn't ask for the minimum if it were just 1 (that would make for a boring problem, and they'll do that sometimes, but very rarely).

 

Since we're looking for the minimum value any of one of them could take, we can plug in the maximum value for the other three numbers. This forces the last number to be the smallest it can possibly be. We know the relationship between the numbers is that their average is 94. Using x to represent the unknown smallest number, we can write this as:

 

(x+99+99+99)/4=94

 

Then, we add up the three 99s to get

 

(x+297)/4=94

 

Multiply both sides by 4 and we get

 

x+297=376

 

And finally, we can subtract 297 on both sides to get

 

x=79.

 

Hope this helps!

Answer 2

The lowest value will be the the most extreme case where three of the other numbers are 99. This leaves (99*3 + x)/4 = 94.

 

99*3 + x = 376

 

297 + x = 376

 

x = 79