If the average (arithmetic mean) of five distinct positive integers is 10, what is the difference between the largest possible value of the greatest integer and the least possible value of the greatest of the five integers

The difference between the largest possible value of the greatest integer and the least possible value of the greatest of the five integers = 4

Step-by-step explanation:

Step 1:-

let 'x' be the number

The sequence of arithmetic progression of distinct positive integers

x , x+1 , x+2 , x+3 , x+4

Given the average of five distinct positive integers is 10

on simplification , and cross multiplication , we get

5x +10 = 5 X10

5x +10 =50

subtracting'10' on both sides, we get

5x +10 - 10 = 50 -10

5x =40

dividing '5' on both sides, we get

x = 8

The number is '8'

Step 2:-

Now the arithmetic sequence of five numbers are

x , x+1 , x+2 , x+3 , x+4

8 , 9, 10 , 11 , 12

In this sequence is smallest number is '8' and

The largest number is '12'

the difference between the largest possible value of the greatest integer and the least possible value of the greatest of the five integers

= largest possible value - least possible value

= 12 - 8 =4

Final answer = 4

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10