SOLUTION: which number between 50 and 60 can be divided into four parts so that if you multiply the first part by 2,add 2 to the second part ,subtract 2 from the third part and divide the fo

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Question 714770: which number between 50 and 60 can be divided into four parts so that if you multiply the first part by 2,add 2 to the second part ,subtract 2 from the third part and divide the fourth part by 2,the result will be the same.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B2 = 2 added to the second part
y-2 = 2 subtracted from the third part
z%2F2 = fourth part divided by 2

2w=x%2B2=y-2=z%2F2
We can express all four parts as a function of w :
2w=x%2B2 --> 2w-2=x
2w=y-2 --> 2w%2B2=y
2w=z%2F2 --> 4w=z

The sum of all four parts is w%2Bx%2By%2Bz=N , an integer such that 50%3C=N%3C=60
N=w%2B%282w-2%29%2B%282w%2B2%29%2B4w=9w
So N is a multiple of 9,
and the only one between 50 and 60 is highlight%2854%29.