document.write( "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.
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Algebra.Com's Answer #590638 by Fombitz(32388) $\"\"$ $\"About$

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1. $\"X%2F237=M%2B112\"$
\n" ); document.write( "2. $\"Y%2F117=N%2B108\"$
\n" ); document.write( "3. $\"X%2F237=Y%2F117\"$
\n" ); document.write( "where $\"M\"$ , $\"N\"$ are integers.
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\n" ); document.write( "From eq. 1,
\n" ); document.write( " $\"X%2F237=M%2B112\"$
\n" ); document.write( " $\"X=237M%2B26544\"$
\n" ); document.write( "From eq. 2,
\n" ); document.write( " $\"Y=17N%2B12636\"$
\n" ); document.write( "From eq. 3,
\n" ); document.write( " $\"M%2B112=N%2B108\"$
\n" ); document.write( " $\"M=N-4\"$
\n" ); document.write( " $\"N=M%2B4\"$
\n" ); document.write( "Then the sum becomes,
\n" ); document.write( " $\"%28X%2BY%29%2F118=%28237M%2B26544%2B117N%2B12636%29%2F118\"$
\n" ); document.write( " $\"%28X%2BY%29%2F118=%28237M%2B26544%2B117%28M%2B4%29%2B12636%29%2F118\"$
\n" ); document.write( " $\"%28X%2BY%29%2F118=%28237M%2B26544%2B117M%2B468%2B12636%29%2F118\"$
\n" ); document.write( " $\"%28X%2BY%29%2F118=%28354M%2B39648%29%2F118\"$
\n" ); document.write( " $\"%28X%2BY%29%2F118=%28354M%2F118%29%2B%2839648%2F118%29\"$
\n" ); document.write( " $\"%28X%2BY%29%2F118=3M%2B336\"$
\n" ); document.write( "The remainder is zero.\r
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