document.write( "Question 1162454: What is the greatest integer, which when divided into 383, 527, or 815 leaves the same remainder? \n" ); document.write( "
Algebra.Com's Answer #786264 by Edwin McCravy(20067)\"\" \"About 
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What is the greatest integer, which when divided into 383, 527, or 815
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document.write( "Let the greatest integer be d, and the common remainder be r.  Then\r\n" );
document.write( "Let q1, q2, q3 be the quotients. Then\r\n" );
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document.write( "\"system%28q%5B1%5Dd%2Br=383%2Cq%5B2%5Dd%2Br=527%2C+q%5B3%5Dd%2Br=815%29\"\r\n" );
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document.write( "Solving the first two equations for r:\r\n" );
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document.write( "That tells us that the most d can be is 144, and it can be 144 if we can get\r\n" );
document.write( "the denominator q2-q1 to equal 1.\r\n" );
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document.write( "Solving the first and third equations for r:\r\n" );
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document.write( "Solving the second and third equations for r:\r\n" );
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document.write( "So d can be 144 if we can have \r\n" );
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document.write( "q2-q1 = 1\r\n" );
document.write( "q3-q1 = 3\r\n" );
document.write( "q3-q2 = 2\r\n" );
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document.write( "Solving that dependent system, we get\r\n" );
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document.write( "\"%28matrix%281%2C5%2Cq%5B1%5D%2C%22%2C%22%2Cq%5B2%5D%2C%22%2C%22%2Cq%5B3%5D%29%29\"\"%22%22=%22%22\"\"%28matrix%281%2C5%2Cq%5B3%5D-3%2C%22%2C%22%2Cq%5B3%5D-2%2C%22%2C%22%2Cq%5B3%5D%29%29\"\r\n" );
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document.write( "So if we let q3=4, we have\r\n" );
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document.write( "\"%28matrix%281%2C5%2Cq%5B1%5D%2C%22%2C%22%2Cq%5B2%5D%2C%22%2C%22%2Cq%5B3%5D%29%29\"\"%22%22=%22%22\"\"%28matrix%281%2C5%2C1%2C%22%2C%22%2C2%2C%22%2C%22%2C4%29%29\"\r\n" );
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document.write( "We can have the maximum of \"d=144%2F%282-1%29=144\"\r\n" );
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document.write( "Edwin
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