document.write( "Question 473824: The reverse of a two digit number is the number obtained by writing the digits in reverse order. For example, 37 is the reverse of 73, and 44 is its own reverse. How many three digit numbers are the product of two 2-digit numbers which are reverses of each other? The number 252 is an example since 12*21 =252. choose the answer and explain the reason to choose your response
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\n" ); document.write( "more than 10
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Algebra.Com's Answer #325021 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The smallest possible case is 11×11 = 121\r\n" );
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document.write( "Let the the maximal digit be x and the minimal digit be y\r\n" );
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document.write( "x ≧ y\r\n" );
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document.write( "The product is\r\n" );
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document.write( "(10x + y)(10y + x) < 1000\r\n" );
document.write( "100xy+10x²+10y²+xy < 1000 \r\n" );
document.write( "   10x²+101xy+10y² < 1000\r\n" );
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document.write( "Let y, the minimal digit, be small as possible, i.e., y=1\r\n" );
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document.write( "   10x²+101x+10 < 1000\r\n" );
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document.write( "   10x²+100x-990 < 0\r\n" );
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document.write( "The solution to that quadratic inequality is\r\n" );
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document.write( "-16.14 < x < 6.13\r\n" );
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document.write( "But since x is an integer, x = 1,2,3,4,5, or 6\r\n" );
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document.write( "61×16 = 976, and that is a 3-digit number\r\n" );
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document.write( "So\r\n" );
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document.write( "61×16, 51×15, 41×14, 31×13, 21×12, and 11×11\r\n" );
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document.write( "account for 6 cases.\r\n" );
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document.write( "Let y, be the next smallest digit possible i.e., y=2\r\n" );
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document.write( "   10x²+101xy+10y² < 1000\r\n" );
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document.write( "   10x²+101x(2)+10(2)² < 1000\r\n" );
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document.write( "          10x²+202x-40 < 1000\r\n" );
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document.write( "        10x²+202x-1040 < 0     \r\n" );
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document.write( "The solution to that quadratic inequality is\r\n" );
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document.write( "-24.45 < x < 4.25\r\n" );
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document.write( "Since x is an integer, x = 1,2,3, or 4\r\n" );
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document.write( "But 42×24 = 1008, is too large\r\n" );
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document.write( "However,\r\n" );
document.write( "32×23 = 736 and 22×22 = 484 account for 2 more cases.\r\n" );
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document.write( "That's 8 cases.\r\n" );
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document.write( "The minimal digit y cannot be 3 since 33×33=1089,\r\n" );
document.write( "which is not a 3 digit number.\r\n" );
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document.write( "So there are only 8 such 3-digit products.\r\n" );
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document.write( "Answer: fewer than 9.  In fact there are only these 8\r\n" );
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document.write( "61×16 = 976\r\n" );
document.write( "51×15 = 765\r\n" );
document.write( "41×14 = 574\r\n" );
document.write( "31×13 = 403\r\n" );
document.write( "21×12 = 252\r\n" );
document.write( "11×11 = 121\r\n" );
document.write( "22×22 = 484\r\n" );
document.write( "23×32 = 736\r\n" );
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document.write( "Edwin
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