Question 714770
It is not clearly specified, but I am sure that the number and its four parts are understood to be integers.
The person who proposed the problem understands it that way, and we have to understand it too.
 
{{{w}}} = first part
{{{x}}} = second part
{{{y}}} = third part
{{{z}}} = fourth part
 
{{{2w}}} = first part multiplied by 2
{{{x+2}}} = 2 added to the second part
{{{y-2}}} = 2 subtracted from the third part
{{{z/2}}} = fourth part divided by 2
 
{{{2w=x+2=y-2=z/2}}}

We can express all four parts as a function of {{{w}}} :
{{{2w=x+2}}} --> {{{2w-2=x}}}
{{{2w=y-2}}} --> {{{2w+2=y}}}
{{{2w=z/2}}} --> {{{4w=z}}}
 
The sum of all four parts is {{{w+x+y+z=N}}} , an integer such that {{{50<=N<=60}}}
{{{N=w+(2w-2)+(2w+2)+4w=9w}}}
So {{{N}}} is a multiple of 9,
and the only one between 50 and 60 is {{{highlight(54)}}}.