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The average of four different positive whole numbers is 4. If the difference between the largest and smallest of these numbers is as large as possible, what is the average of the other two numbers?

SmartMathMan  Dec 7, 2017

Best Answer 

 #1
avatar+7324 
+1

( n1  +  n2  +  n3  +  n4 ) / 4   =   4          so          n1  +  n2  +  n3  +  n4   =   16

 

For the difference between the largest and smallest number to be as large as possible, the smallest number needs to be as small as possible, and the largest number needs to be as large as possible.

 

The smallest positive whole number is  1 , so    n1  =  1

 

For  n4  to be as large as possible, we also need  n2  and  n3  to be as small as possible.

 

It says that the numbers have to be different, so

 

n2  =  2     and   n3  =  3

 

That makes  n4  be  10 .

 

( n2 + n3 ) / 2   =   (2 + 3) / 2   =   2.5

hectictar  Dec 7, 2017
 #1
avatar+7324 
+1
Best Answer

( n1  +  n2  +  n3  +  n4 ) / 4   =   4          so          n1  +  n2  +  n3  +  n4   =   16

 

For the difference between the largest and smallest number to be as large as possible, the smallest number needs to be as small as possible, and the largest number needs to be as large as possible.

 

The smallest positive whole number is  1 , so    n1  =  1

 

For  n4  to be as large as possible, we also need  n2  and  n3  to be as small as possible.

 

It says that the numbers have to be different, so

 

n2  =  2     and   n3  =  3

 

That makes  n4  be  10 .

 

( n2 + n3 ) / 2   =   (2 + 3) / 2   =   2.5

hectictar  Dec 7, 2017

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