Question

A number is 56 greater than the average of its third, quarter and one twelfth part find the number

Answer 1

let the number be x
so,
(x/3+x/4+x/12)/3=x-56
(4x+3x+x)3/12=x-56
8x/4=x-56
2x=x-56
2x-x=-56
x=-56

Answer 2

((1/3x +1/4x + 1/12x) /3) + 56 = x 

multiply both sides by 3 
1/3x + 1/4x + 1/12x + 168 = 3x 

multiply boths sides by 12 to get rid of the fractional components 

4x + 3x + x + 2016 = 36x 

add the x's and take away 2016 

8x = 36x - 2016 

x = 4.5x - 252 

take away 4.5 x 

-3.5x = -252 

x = 72 

check 

1/4x = 18 
1/3x = 24 
1/12x = 6 

average (18 + 24 + 6)/3 = 16 

16 + 56 = x = 72