document.write( "Question 892975: Mico's house number has three digits. Removing the leftmost digit gives Ben's house number. Removing the leftmost digit of Ben's house number gives Ciara's house number. The sum of the three house numbers is 912. What is the middle digit of Mico's house number? \n" ); document.write( "

Algebra.Com's Answer #540965 by Edwin McCravy(20060) $\"\"$ $\"About$

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Mico's house number has three digits. Removing the leftmost digit gives Ben's
\n" ); document.write( "house number. Removing the leftmost digit of Ben's house number gives Ciara's
\n" ); document.write( "house number. The sum of the three house numbers is 912. What is the middle
\n" ); document.write( "digit of Mico's house number?
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document.write( "Let h = the hundreds digit (of Mico's house number)\r\n" );
document.write( "Let t = the tens digit \r\n" );
document.write( "Let u = the units digit\r\n" );
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document.write( "So the house numbers written in digit form are \r\n" );
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document.write( "Mico's house number = htu.\r\n" );
document.write( "Ben's house number = tu.\r\n" );
document.write( "Clara's house number = u.\r\n" );
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document.write( "We form the arithmetic (basic math) addition:\r\n" );
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document.write( "htu\r\n" );
document.write( " tu\r\n" );
document.write( "  u\r\n" );
document.write( "---\r\n" );
document.write( "912\r\n" );
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document.write( "In the right column To get the 2 at the bottom, the 3 u's have \r\n" );
document.write( "to be 4 so they'll add up to 12 and there'll be 1 to carry.  So \r\n" );
document.write( "we have this:\r\n" );
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document.write( " 1\r\n" );
document.write( "ht4\r\n" );
document.write( " t4\r\n" );
document.write( "  4\r\n" );
document.write( "---\r\n" );
document.write( "912\r\n" );
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document.write( "Looking at the middle column of digits, either the two t's are 0 \r\n" );
document.write( "so the middle column of digits will add up to 1, or the two t's \r\n" );
document.write( "are 5 so that the middle column will add up to 11 with 1 to carry.\r\n" );
document.write( "But t can't be 0 because that would make Ben's house number 04.  \r\n" );
document.write( "But nobody writes 04, they just write 4.  So if you removed the \r\n" );
document.write( "leftmost digit of 4 you would have nothing at all!  So 0 is out.\r\n" );
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document.write( "Therefore t = 5  (That's the answer).\r\n" );
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document.write( "Completing the addition:\r\n" );
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document.write( "11\r\n" );
document.write( "h54\r\n" );
document.write( " 54\r\n" );
document.write( "  4\r\n" );
document.write( "---\r\n" );
document.write( "912 \r\n" );
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document.write( "Since we have 1 to carry to the left column,\r\n" );
document.write( "which gives us a 9 at the bottom left, h can \r\n" );
document.write( "only be 8.\r\n" );
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document.write( "11\r\n" );
document.write( "854\r\n" );
document.write( " 54\r\n" );
document.write( "  4\r\n" );
document.write( "---\r\n" );
document.write( "912\r\n" );
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document.write( "The house numbers are 854, 54, and 4 and the \r\n" );
document.write( "middle digit of Mico's house number is 5.\r\n" );
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document.write( "Edwin

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