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

#1**+1 **

( n_{1} + n_{2} + n_{3} + n_{4} ) / 4 = 4 so n_{1} + n_{2} + n_{3} + n_{4} = 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 n_{1} = 1

For n_{4} to be as large as possible, we also need n_{2} and n_{3} to be as small as possible.

It says that the numbers have to be different, so

n_{2} = 2 and n_{3} = 3

That makes n_{4} be 10 .

( n_{2} + n_{3} ) / 2 = (2 + 3) / 2 = 2.5

hectictar
Dec 7, 2017

#1**+1 **

Best Answer

( n_{1} + n_{2} + n_{3} + n_{4} ) / 4 = 4 so n_{1} + n_{2} + n_{3} + n_{4} = 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 n_{1} = 1

For n_{4} to be as large as possible, we also need n_{2} and n_{3} to be as small as possible.

It says that the numbers have to be different, so

n_{2} = 2 and n_{3} = 3

That makes n_{4} be 10 .

( n_{2} + n_{3} ) / 2 = (2 + 3) / 2 = 2.5

hectictar
Dec 7, 2017