document.write( "Question 1208966: the numbers on the houses on the north side of carlito street are consecutive odd starting with 1. The plastic digits used to label each house are $0.04 per digit. If it costs $58.12 to label all the houses on the north side of Carlito street, how many houses are there? \n" ); document.write( "
Algebra.Com's Answer #847513 by mccravyedwin(408)\"\" \"About 
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document.write( "Let's pretend they put plastic digits on ALL the houses on both sides of the\r\n" );
document.write( "street. and that there are the same number of houses on both sides of the\r\n" );
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document.write( "The number of digits in all the even integers 0,2,...,2n is the same as the\r\n" );
document.write( "number of digits in all the odd integers 1,3,...,2n+1\r\n" );
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document.write( "It would have cost twice as much, $58.12x2 = $116.24, to put plastic digits on\r\n" );
document.write( "all the houses on both the north and south sides of the street, that is, IF the\r\n" );
document.write( "first even-numbered house were numbered 0.\r\n" );
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document.write( "[Even though 0 is not normally used as a house number, let's pretend it is\r\n" );
document.write( "on this street anyway.]\r\n" );
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document.write( "If we consider 0 as a 1-digit number, then\r\n" );
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document.write( "there are 10 1-digit numbers which would cost $0.04x10=$0.40,\r\n" );
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document.write( "there are 100-10=90 2-digit numbers which would cost $0.04x2x90=$7.20,\r\n" );
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document.write( "and there are 1000-100=900 3-digit numbers which would cost $0.04x3x900=$108.\r\n" );
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document.write( "That would cost $0.40+$7.20+$108=$115.60\r\n" );
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document.write( "Since $116.24-115.60=$0.64, that means they placed $0.64/$0.04 = 16 more\r\n" );
document.write( "plastic digits than they placed on houses numbered with 3 or fewer digits.\r\n" );
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document.write( "So 16 plastic digits were placed on 4 houses with 4-digit numbers.\r\n" );
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document.write( "These are the houses numbered 1000, 1001, 1002, and 1003.\r\n" );
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document.write( "So the even house numbers are 0,2,4,...,1002 and there are 1002/2=501 of them.\r\n" );
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document.write( "The odd house numbers are 1,3,5,...,1003 and there are also 501 of them. \r\n" );
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document.write( "Answer: There are 501 odd numbered houses on the north side of the street.\r\n" );
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document.write( "Edwin
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