SOLUTION: there are two positive integers x and y. when X is divided by 237, the remainder is 192. When Y is divided by 117 the quotient is the same but the remainder is 108. Find the remain

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Question 966372: there are two positive integers x and y. when X is divided by 237, the remainder is 192. When Y is divided by 117 the quotient is the same but the remainder is 108. Find the remainder when the sum of X and Y is divided by 118.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.X%2F237=M%2B112
2.Y%2F117=N%2B108
3.X%2F237=Y%2F117
where M, N are integers.
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From eq. 1,
X%2F237=M%2B112
X=237M%2B26544
From eq. 2,
Y=17N%2B12636
From eq. 3,
M%2B112=N%2B108
M=N-4
N=M%2B4
Then the sum becomes,
%28X%2BY%29%2F118=%28237M%2B26544%2B117N%2B12636%29%2F118
%28X%2BY%29%2F118=%28237M%2B26544%2B117%28M%2B4%29%2B12636%29%2F118
%28X%2BY%29%2F118=%28237M%2B26544%2B117M%2B468%2B12636%29%2F118
%28X%2BY%29%2F118=%28354M%2B39648%29%2F118
%28X%2BY%29%2F118=%28354M%2F118%29%2B%2839648%2F118%29
%28X%2BY%29%2F118=3M%2B336
The remainder is zero.