document.write( "Question 823921: How many two digit whole numbers are increased by 18 when they are reversed? What are they?
\n" ); document.write( "So far, the only number i have is 13 because when reversed its 31 and 13 plus 18 is 31. Please help me. I have gone up to 25 and found no other number \n" ); document.write( "
Algebra.Com's Answer #495937 by Edwin McCravy(20060)\"\" \"About 
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How many two digit whole numbers are increased by 18
\n" ); document.write( "when they are reversed? What are they?\r
\n" ); document.write( "\n" ); document.write( "So far, the only number i have is 13 because when reversed its 31 and 13 plus 18 is 31. Please help me. I have gone up to 25 and found no other number.
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document.write( "Then you will either --\r\n" );
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document.write( "have to keep trying two-digit numbers from the smallest\r\n" );
document.write( "two-digit number, 10, all the way through the largest one, 99, and add 18 to\r\n" );
document.write( "every one of them to see if the answer is the number with the digits reversed.  \r\n" );
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document.write( "Or else --\r\n" );
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document.write( "you can do a little algebra. \r\n" );
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document.write( "Let t= the tens digit and u= the units or ones digit.\r\n" );
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document.write( "Then (10t+u) is the two digit number.\r\n" );
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document.write( "and (10u+t) is its reverse.\r\n" );
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document.write( "So we increase (10t+u) by 18 and we get the reverse, (10u+t)\r\n" );
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document.write( "To say that in algebra,\r\n" );
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document.write( "(10t+u) + 18 = (10u+t)\r\n" );
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document.write( "    10t+u+18 = 10u+t\r\n" );
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document.write( "    9t-9u+18 = 0\r\n" );
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document.write( "Divide through by 9\r\n" );
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document.write( "   t - u + 2 = 0\r\n" );
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document.write( "Add u to both sides:\r\n" );
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document.write( "        t + 2 = u\r\n" );
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document.write( "That formula is saying \"You have to add 2 to the ten's digit \r\n" );
document.write( "to get the units digit\".  So we have to choose the tens digit \r\n" );
document.write( "from 1 through 7, because you can't add 2 to 8 or 9 and get \r\n" );
document.write( "a single digit, because you have to then choosethe units digit\r\n" );
document.write( "as 2 more than the tens digit.  So we just have these 7 numbers:\r\n" );
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document.write( "13, 24, 35, 46, 57, 68, 79\r\n" );
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document.write( "Let's test them all:\r\n" );
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document.write( "13+18=31 That reverses when you add 18.\r\n" );
document.write( "24+18=42  \"        \"     \"   \"   \"   \" \r\n" );
document.write( "35+18=53  \"        \"     \"   \"   \"   \"      \r\n" );
document.write( "46+18=64  \"        \"     \"   \"   \"   \"\r\n" );
document.write( "57+18=75  \"        \"     \"   \"   \"   \"        \r\n" );
document.write( "68+18=86  \"        \"     \"   \"   \"   \"\r\n" );
document.write( "79+18=97  \"        \"     \"   \"   \"   \"\r\n" );
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document.write( "So they all reverse the number when you add 18.  \r\n" );
document.write( "That was better than having to add 18 to them all\r\n" );
document.write( "the way from 10 to 99. \r\n" );
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document.write( "But you really even don't have to do all the above \r\n" );
document.write( "every time.  You can just look at the equation \r\n" );
document.write( "t + 2 = u  and see there are only 7 solutions in \r\n" );
document.write( "positive integers, because t can't run over 7, so\r\n" );
document.write( "t can only be an integer from 1 through 7.\r\n" );
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document.write( "Edwin
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