Question

The average of three numbers is 42.the first is twice the second and second is twice the third . the difference between the largest and the smallest number is

Answer 1

Answer:

The difference between the largest and the smallest number = 54

Step-by-step explanation:

Let x, y and z be the three numbers.

Given:

(x+y+z) / 3 = 42

x+y+z = 126 ...... equ 1

x = 2y

y = 2z

To find:

The difference between the largest and the smallest number

substitute x=2y in equ 1

=> 2y + y + z = 126

3y + z = 126..... equ 2

substitute y = 2z in equ 2

=> 6z + z = 126

7z = 126

z = 126/7 = 18

substitute z = 18 in equ 2

3y + 18 = 126

3y = 126 - 18 = 108

y = 108/3 = 36

substitute y = 36 and z = 18 in equ 1

x + 36 + 18 = 126

x + 54 = 126

x = 126-54 = 72

The three numbers are 72, 36 and 18.

Largest number = 72

Smallest number = 18

The difference between the largest and the smallest number = 72 - 18 = 54

Hope it helps you:)