document.write( "Question 975899: what is the three digit number that satisfies the following condition.the tens digit is greater than the ones digit, the sum of the digits is 9 and if digits are reversed and resulting three-digit number is subtracted from the original number, the difference is 198 \n" ); document.write( "
Algebra.Com's Answer #597548 by Edwin McCravy(20056)\"\" \"About 
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what is the three digit number that satisfies the following condition.the tens
\n" ); document.write( "digit is greater than the ones digit, the sum of the digits is 9 and if digits
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document.write( "Let the number be ABC and its reverse be CBA,\r\n" );
document.write( "Then the subtraction is:\r\n" );
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document.write( " ABC\r\n" );
document.write( "-CBA\r\n" );
document.write( " ---\r\n" );
document.write( " 198\r\n" );
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document.write( "A must be bigger than C so that the top number will be bigger than the bottom\r\n" );
document.write( "number.  So we will need to borrow 1 from the B at the start of the subtraction.\r\n" );
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document.write( "That will reduce the B in the top middle digit to 1 less than the B just below\r\n" );
document.write( "it.\r\n" );
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document.write( "Therefore we will also need to borrow 1 from the A as well.\r\n" );
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document.write( "If we had not needed to borrow 1 from the A, then A-C would have been 1 to\r\n" );
document.write( "get the 1 in 198.  But since we must borrow 1 from A, A-C must be 2\r\n" );
document.write( "instead, so that borrowing 1 from A would give the 1 in 198.\r\n" );
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document.write( "A-C cannot be as high as 6-4 because all three digits must have sum 9,\r\n" );
document.write( "and 6 and 4 alone have sum 10.  So we try lower digits.\r\n" );
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document.write( "We try A-C = 5-3, making the number 513 since the digits must have sum 9.\r\n" );
document.write( "But that won't do because the tens digit is less than the ones digit.\r\n" );
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document.write( "We try A-C = 4-2. Then the number would be 432 since the digits must have sum 9.\r\n" );
document.write( "That's one solution because the tens digit is greater than the ones digit, and\r\n" );
document.write( "432-234=198.\r\n" );
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document.write( "We try A-C = 3-1. Then the number would be 351 since the digits must have sum 9. \r\n" );
document.write( "That's another solution because the tens digit is greater than the ones digit,\r\n" );
document.write( "and 351-153 = 198.\r\n" );
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document.write( "So there are TWO solutions, 432 and 351\r\n" );
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document.write( " 432          351\r\n" );
document.write( "-234         -153\r\n" );
document.write( "----         ----\r\n" );
document.write( " 198          198\r\n" );
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document.write( "Edwin
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