document.write( "Question 554011: The difference between a number consisting of two digits and the number formed by reversing the digits is 45. The sum of three times the tens digit and five times the units is 47. Find the number \n" ); document.write( "
Algebra.Com's Answer #361159 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
The difference between a number consisting of two digits and the number formed by reversing the digits is 45.
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document.write( "There are only 4 such numbers:\r\n" );
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document.write( "61, since 61 - 16 = 45\r\n" );
document.write( "72, since 72 - 27 = 45\r\n" );
document.write( "83, since 83 - 38 = 45\r\n" );
document.write( "94, since 94 - 49 = 45\r\n" );
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\n" ); document.write( "The sum of three times the tens digit and five times the units is 47. There
\n" ); document.write( "are only 2 such numbers:
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document.write( "47, since 3*4 + 5*7 = 12 + 35 = 47\r\n" );
document.write( "94, since 3*9 + 5*4 = 27 + 20 = 47\r\n" );
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document.write( "So the only 2-digit number having both properties is 94.\r\n" );
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document.write( "But your teacher will not accept that method.  \r\n" );
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document.write( "Here's how to work it with algebra:\r\n" );
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\n" ); document.write( "The difference between a number consisting of two digits and the number formed by reversing the digits is 45.
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document.write( "(10t + u) - (10u + t) = 45\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "    10t + u - 10u - t = 45\r\n" );
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document.write( "Collect like terms:\r\n" );
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document.write( "              9t - 9u = 45\r\n" );
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document.write( "Divide through by 9:\r\n" );
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document.write( "                t - u = 5 \r\n" );
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\n" ); document.write( "The sum of three times the tens digit and five times the units is 47.
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document.write( "              3t + 5u = 47\r\n" );
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document.write( "Solve the system of equations:\r\n" );
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document.write( "               t -  u =  5\r\n" );
document.write( "              3t + 5u = 47\r\n" );
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document.write( "Solve the first for t:\r\n" );
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document.write( "                t - u =  5\r\n" );
document.write( "                    t = 5 + u\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "              3t + 5u = 47\r\n" );
document.write( "        3(5 + u) + 5u = 47\r\n" );
document.write( "         15 + 3u + 5u = 47\r\n" );
document.write( "                   8u = 32 \r\n" );
document.write( "                    u = 4\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "                    t = 5 + u  \r\n" );
document.write( "                    t = 5 + 4\r\n" );
document.write( "                    t = 9\r\n" );
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document.write( "number = 10t + u = 10(9) + 4 = 94 \r\n" );
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document.write( "Edwin

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