document.write( "Question 1184950: The unit digit of a two digit number is 1 less than the tens digit. If the number is increased by 8 and then divided by the sum of the digits, the result is 8. Find the number. \n" ); document.write( "

Algebra.Com's Answer #815655 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "The unit digit of a two digit number is 1 less than the tens digit.
\n" ); document.write( "If the number is increased by 8 and then divided by the sum of the digits, the result is 8.
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document.write( "Let the \"tens\" digit be t.\r\n" );
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document.write( "Then the \"units\" difit is (t-1), according to the condition.\r\n" );
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document.write( "Hence, the number itself is  N = 10t + (t-1).\r\n" );
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document.write( "Then the number N+8 is  10t + (t-1) + 8 = 10t + t + 7 = 11t + 7.\r\n" );
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document.write( "From the last statement of the problem, we have this equation\r\n" );
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document.write( "    N+8 = 8*(t+u),\r\n" );
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document.write( "or\r\n" );
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document.write( "    11t + 7 = 8*(t+(t-1)).\r\n" );
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document.write( "Simplify and find t\r\n" );
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document.write( "    11t + 7 = 8*(2t-1)\r\n" );
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document.write( "    11t + 7 = 16t - 8\r\n" );
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document.write( "      7 + 8 = 16t - 11t\r\n" );
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document.write( "       15   =    5t\r\n" );
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document.write( "        t   =    15/5 = 3.\r\n" );
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document.write( "Thus the tens digit is 3;  the units digit is 3-1 = 2;  and the number itself is  32.    ANSWER\r\n" );
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