document.write( "Question 1110921: A two-digit number is 2 more than 8 times the sum of its digits. Find the number if its tens digit is 6 more than its unit digit. \n" ); document.write( "

Algebra.Com's Answer #725931 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "Answer.  82.\r\n" );
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document.write( "Let the decimal form of the number is \"ab\".\r\n" );
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document.write( "Then \r\n" );
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document.write( "10a + b = 2 + 8*(a+b)      (\"A two-digit number is 2 more than 8 times the sum of its digits\")\r\n" );
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document.write( "10a + b = 2 + 8a + 8b,\r\n" );
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document.write( "2a = 2 + 7b.      (1)\r\n" );
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document.write( "Also,\r\n" );
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document.write( "a = 6 + b          (2)      (\"tens digit is 6 more than unit digit\")\r\n" );
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document.write( "Substitute (2) into (1). You will get\r\n" );
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document.write( "12 + 2b = 2 + 7b,\r\n" );
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document.write( "10 = 5b  ====>  b = 2.\r\n" );
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document.write( "Then a = b+6 = 2 + 6 = 8,   and you get the answer.\r\n" );
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