document.write( "Question 41905: Mr and Mrs Wombat live in a house in which the floor of every room is a square and covered with identical tiles. Mrs Wombat's room contains 101 tiles more than Mr Wombat's room. How many tiles does Mrs Wombat's room contain? \n" ); document.write( "
Algebra.Com's Answer #27027 by AnlytcPhil(1810)\"\" \"About 
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Mr and Mrs Wombat live in a house in which the floor of \r\n" );
document.write( "every room is a square and covered with identical tiles. \r\n" );
document.write( "Mrs Wombat's room contains 101 tiles more than Mr Wombat's \r\n" );
document.write( "room. How many tiles does Mrs Wombat's room contain?\r\n" );
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document.write( "Let x = number of tiles in each side of Mr. Wombat's room\r\n" );
document.write( "Let y = number of tiles in each side of Mrs. Wombat's room\r\n" );
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document.write( "Then there are x² tiles in Mrs. Wombat's room.\r\n" );
document.write( "And there are y² tiles in Mr. Wombat's room.\r\n" );
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document.write( ">>...Mrs. Wombat's room contains 101 tiles more than Mr. \r\n" );
document.write( "Wombat's room...<<\r\n" );
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document.write( "             y² = x² + 101\r\n" );
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document.write( "        y² - x² = 101\r\n" );
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document.write( " (y - x)(y + x) = 101\r\n" );
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document.write( "The two parentheses on the left must be a factorization\r\n" );
document.write( "of 101.  Since 101 is a prime number, its only \r\n" );
document.write( "factorization is  1×101. Since (y - x) is smaller than\r\n" );
document.write( "(y + x), we must have\r\n" );
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document.write( "           y - x = 1\r\n" );
document.write( "and \r\n" );
document.write( "           y + x = 101\r\n" );
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document.write( "So we have this system\r\n" );
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document.write( "           y - x = 1\r\n" );
document.write( "           y + x = 101\r\n" );
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document.write( "Solving that gives x = 51 and y = 50 \r\n" );
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document.write( "So Mrs. Wombat's room has 51 tiles on each side and\r\n" );
document.write( "Mr. Wombat's room has 50 tiles on each side.\r\n" );
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document.write( "The question is:\r\n" );
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document.write( ">>...How many tiles does Mrs Wombat's room contain?...<<\r\n" );
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document.write( "So her room has 51×51 or 2601 tiles\r\n" );
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document.write( "Checking:\r\n" );
document.write( "Mrs. Wombat's room has 2601 tiles\r\n" );
document.write( "Mr. Wombat's room has 50×50 of 2500 tiles\r\n" );
document.write( "Since 2601 is 101 more than 2500, the solution is correct.\r\n" );
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document.write( "Edwin McCravy\r\n" );
document.write( "AnlytcPhil@aol.com

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