document.write( "Question 86887This question is from textbook algebra structure and method
\n" ); document.write( ": I'm not sure how to take a story problem and put it into a equation. could you help!!
\n" ); document.write( "When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?
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Algebra.Com's Answer #62831 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
I'm not sure how to take a story problem and put it into a equation. could you
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\n" ); document.write( "When the digits of a two-digit number are reversed, the new number is 9 more
\n" ); document.write( "than the original number, and the sum of the digits of the original number is
\n" ); document.write( "11. What is the original number?
\n" ); document.write( "Help!!!!
\n" ); document.write( "How would you check it also?
\n" ); document.write( "Thanks so much!!!
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document.write( "First notice that a two digit number like 74 is such that if you take the fist\r\n" );
document.write( "digit 7, multiply it by 10, you get 70, and then if you add the second digit,\r\n" );
document.write( "4,  to the 70, you get the number 74.   74 = 10×7 + 4\r\n" );
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document.write( "Another example: Notice that a two digit number like 29 is such that if you\r\n" );
document.write( "take the fist digit 2, multiply it by 10, you get 20, and then if you add the\r\n" );
document.write( "second digit 9 to the 20, you get the number 29.   28 = 10×2 + 9\r\n" );
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document.write( "Therefore, it's easy to see that \r\n" );
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document.write( "any 2-digit number = \r\n" );
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document.write( "          10 times its first digit + its second digit.\r\n" );
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document.write( "Let x = the first digit and y = the second digit.\r\n" );
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document.write( "Then the number = 10x + y and\r\n" );
document.write( "the number reversed = 10y + x\r\n" );
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document.write( ">>...the sum of the digits of the original number \r\n" );
document.write( "is 11...<<\r\n" );
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document.write( "x + y = 11\r\n" );
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document.write( ">>...When the digits of a two-digit number are \r\n" );
document.write( "reversed, the new number is 9 more than the original \r\n" );
document.write( "number...<<\r\n" );
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document.write( "(10y + x) = (10x + y) + 9\r\n" );
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document.write( "simplifying:\r\n" );
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document.write( "  10y + x = 10x + y + 9\r\n" );
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document.write( "  9y - 9x = 9\r\n" );
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document.write( "Dividing thru by 9\r\n" );
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document.write( "    y - x = 1 \r\n" );
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document.write( "So you have this system if equations:\r\n" );
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document.write( "x + y = 11\r\n" );
document.write( "y - x = 1\r\n" );
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document.write( "Solve that by substitution and get x=5, y=6\r\n" );
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document.write( "So the number is 56.\r\n" );
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document.write( "Checking in the words:\r\n" );
document.write( "When the digits of 56 are reversed, you get the \r\n" );
document.write( "new number 65, and that is indeed 9 more than 56, \r\n" );
document.write( "and the sum of the digits of 56 is 5+6 which \r\n" );
document.write( "indeed does equal 11.\r\n" );
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document.write( "Edwin
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