document.write( "Question 116189: the word problem is \" Mosley Hills has reserved the digits 444, 445, and 446 as the prefixes for their phone number. How many different phone numbers are possible? \n" ); document.write( "
Algebra.Com's Answer #84516 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!

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\n" ); document.write( "MISINTERPRETED THE PROBLEM.
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\n" ); document.write( "HERE IS THE CORRECT SOLUTION:
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document.write( "the word problem is \" Mosley Hills has reserved the digits 444, 445, and 446\r\n" );
document.write( "as the prefixes for their phone number. How many different phone numbers are\r\n" );
document.write( "possible?\r\n" );
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document.write( "Here are three methods.  The way to do it depends on what you are\r\n" );
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document.write( "Method 1. \r\n" );
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document.write( "The number of integers from integer M to integer N, inclusive of both, where\r\n" );
document.write( "M < N is N - M + 1. (You have to add the 1 to N - M because when you subtract\r\n" );
document.write( "M from N, you are discounting all the numbers up through M, so you have to \r\n" );
document.write( "add 1 to recount the M.)\r\n" );
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document.write( "The smallest phone number possible is 4440000.  The largest phone number\r\n" );
document.write( "possible is 4469999.  So the number of phone numbers is\r\n" );
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document.write( "4469999 - 4440000 + 1 = 30000\r\n" );
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document.write( "Method 2.\r\n" );
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document.write( "Pick a phone number at random to look at as you think:\r\n" );
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document.write( "445-7338\r\n" );
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document.write( "There is 1 choice for the 1st digit, namely 4.\r\n" );
document.write( "There is 1 choice for the 2nd digit, namely 4.\r\n" );
document.write( "There are 3 choices for the 3rd digit, namely 4,5, or 6.\r\n" );
document.write( "There are 10 choices for the 4th digit, namely 0,1,2,3,4,5,6,7,8, or 9\r\n" );
document.write( "There are 10 choices for the 5th digit, namely 0,1,2,3,4,5,6,7,8, or 9\r\n" );
document.write( "There are 10 choices for the 6th digit, namely 0,1,2,3,4,5,6,7,8, or 9\r\n" );
document.write( "There are 10 choices for the 7th digit, namely 0,1,2,3,4,5,6,7,8, or 9\r\n" );
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document.write( "So the number of phone numbers is 1×1×3×10×10×10×10 = 30,000\r\n" );
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document.write( "Method 3.\r\n" );
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document.write( "The phone numbers:\r\n" );
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document.write( "4440000, 4440001, ..., 4469999\r\n" );
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document.write( "form an arithmetic series with a1 = 4440000, an = 4469999, and\r\n" );
document.write( "common difference d = 1.  We need n, the number of terms.\r\n" );
document.write( "The formula for the nth term of an arithmetic series is\r\n" );
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document.write( "               an = a1 + (n - 1)d\r\n" );
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document.write( "          4469999 = 4440000 + (n - 1)(1)\r\n" );
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document.write( "Solve for n:\r\n" );
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document.write( "          4469999 = 4440000 + n - 1\r\n" );
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document.write( "          4469999 = 4439999 + n \r\n" );
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document.write( "4469999 - 4439999 = n\r\n" );
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document.write( "            30000 = n\r\n" );
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document.write( "Edwin
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